An estimated third of Ukraine’s population has been forced from their homes since Russia invaded in February, including more than 7.1 million people who are displaced inside the country, according to United Nations data, illustrating the scale of a humanitarian crisis that has gone largely unseen as the war grinds on.

The number of internally displaced people dwarfs the 4.8 million Ukrainians who have fled into Europe as refugees, according to the U.N. refugee agency, which has described levels of displacement unseen since World War II.

While large swaths of the country were subject to the brutality of the Russian invasion in its early weeks, most of Ukraine’s displaced are now coming from the east, as that region becomes the center of the conflict.

Boarding trains and buses, civilians have poured out of cities and towns across eastern Ukraine, fleeing for the relative safety of the west and the northern capital, Kyiv. Some have left in humanitarian convoys, navigating treacherous roadways amid the threat of gunfire or shelling. Others have left on foot, literally running for their lives.

And as Russian forces now train their artillery on Donetsk Province in the east, aiming to capture all of the industrial Donbas region, more people are being forced from their homes daily.

“The state was not ready for such a scale of displaced persons in many areas,” Vitaly Muzychenko, the deputy minister of social policy for Ukraine, told a news conference this week, where he announced new plans to register displaced people for state benefits.

Accounting for those in need is a challenge: Just three million people have officially been registered as internally displaced, although the true number is believed to be more than double that. A shortfall in international humanitarian support has further strained local resources.

This mass displacement has reshaped communities across the country, even those that have been spared the physical devastation of the war. Shelters have sprung up in public buildings, university dorms have been converted and some modular homes have been set up to house the displaced.

The majority of internally displaced people, much like refugees, are women and children, and many face shortages of food, water and basic necessities, according to U.N. experts.

Oksana Zelinska, 40, who was the principal of a preschool in the southern city of Kherson, which is now occupied by Russian forces, fled in April with her two children, a co-worker and that woman’s children to the western city of Uzhhorod near the Slovakian border. Her husband has remained behind in Kherson, and she would like to return, but she said she stays in the west for her children.

“When we came here, I needed to do something, it was difficult and I didn’t want to sit around getting depressed,” she said. “I wanted to be useful.”

She began volunteering at the community kitchen that she had used when she first arrived, peeling potatoes and preparing food for the dozens who troop in daily for a hot meal.

Helping the displaced return to their homes — or find new ones — looms as one of Ukraine’s greatest challenges, whatever the outcome of the war. Some of their hometowns may not return to Ukrainian control. Others that are retaken could be almost entirely destroyed, with homes, water lines and other vital infrastructure pulverized by the Russian Army’s scorched-earth tactics.

Ukraine’s government has estimated its reconstruction needs amount to $750 billion. This week, President Volodymyr Zelensky appealed to allies for support by describing the effort as “a joint task of the entire democratic world.” On Tuesday, the United States joined more than 40 governments and multilateral organizations in signing a framework agreement at a conference in Switzerland to help mobilize hundreds of billions of dollars for Ukraine’s recovery, including long-term reconstruction.

It was far from clear whether those pledges would materialize into funds, and how soon. But the host of the meeting, President Ignazio Cassis of Switzerland, declared that the commitments “should give the people in Ukraine hope and the certainty that they are not alone.”

BAKHMUT, Ukraine — With Luhansk Province firmly in Russia’s grasp after weeks of brutal fighting, the country’s military forces on Tuesday were already setting their sights on the next target. On the outskirts of Bakhmut, a key supply hub for Ukrainian forces, the Russian Army was ramping up its shelling as an apparent prelude for an inch-by-inch offensive into the province of Donetsk.

The tactic drove out Ukrainian defenders from the last two cities standing in Luhansk, the other province in the eastern Donbas region, whose capture President Vladimir V. Putin of Russia has described as a crucial objective of his war.

In Sloviansk, one of the cities in Donetsk that lies in Russia’s path, the mayor, Vadym Lyakh, urged residents on Tuesday to flee the city, which he said was now on the front lines. “Artillery is already hitting the city,” he warned in an interview on Ukrainian television, saying that 40 houses were destroyed by shelling the day before. In a Facebook post, he said that one person was killed on Tuesday and seven others wounded in an attack on the city’s central market.

Sloviansk and Bakhmut are likely to be the next cities to face the brunt of the Russian war machine, analysts say. To capture all of Donetsk, Russian forces would most likely need to take Kramatorsk, an administrative center and the headquarters of Ukrainian military forces in the east.

Extent of Russian advance on July 3

Administrative

border

Izium

Sievierodonetsk

Lyman

Lysychansk

Sloviansk

LUHANSK

Kramatorsk

Bakhmut

Popasna

DONETSK

Horlivka

DONBAS

Donetsk

Kyiv

UKRAINE

Detail

area

50 miles

Administrative

border

Izium

Sievierodonetsk

Sloviansk

Lysychansk

LUHANSK

Kramatorsk

Bakhmut

Popasna

DONETSK

Horlivka

DONBAS

Donetsk

Kyiv

UKRAINE

Detail

area

50 miles

Administrative

border

Izium

Sievierodonetsk

Sloviansk

Lysychansk

LUHANSK

Kramatorsk

Bakhmut

Popasna

DONETSK

Horlivka

DONBAS

Donetsk

Kyiv

UKRAINE

Detail

area

50 miles

Sources: Institute for the Study of War with American Enterprise Institute’s Critical Threats Project By Josh Holder

Source: Institute for the Study of War with American Enterprise Institute’s Critical Threats Project.

By Josh Holder

The speaker of the lower house of the Russian Parliament, Vyacheslav Volodin, called for Russian forces to continue their assault, accusing Ukraine without evidence of instigating the fighting.

“They themselves are doing everything to ensure that our troops do not stop at the borders of Luhansk and Donetsk people’s republics,” he said on Tuesday, using the names of the provinces favored by Russia-backed separatists.

Ukraine’s armed forces said Tuesday that Russian troops were focused on restoring transport infrastructure in Luhansk, which has been devastated by months of relentless bombardment, in apparent preparation for a push into Donetsk.

The current phase of Russia’s offensive has been marked by incremental gains backed by withering artillery fire, and Ukrainian forces have often withdrawn from the charred husks of bombed-out cities and towns rather than risk further casualties. It remains to be seen how heavily they will defend cities in Donetsk as they rack up hundreds of dead and wounded soldiers a day and are forced to rely on National Guard units and other less-well-trained fighters.

But Russian forces are also taking heavy losses, and Ukrainian military officials say that their goal is to draw out the fighting in the east as long as possible to exhaust their adversary and buy time until more Western weapons reach the front. In recent days, Ukrainian forces say they have destroyed Russian military infrastructure in occupied areas far from the front lines, a sign that newly arrived, longer-range artillery systems are being put to use.

On Tuesday, Ukraine said it had used one of the most advanced long-range weapons systems provided by the United States — a High Mobility Artillery Rocket System, or HIMARS — to strike Russian ammunition depots in Dibrivne, in the Kharkiv region of Ukraine. That was around 40 miles inside territory controlled by separatists loyal to Russia.

But any ability of Ukrainian troops in the field, many of whom have been under continuous shelling for weeks and even months, and have been taking heavy casualties, to follow up with counterattacks is in deep question.

Andrew E. Kramer and Maria Varenikova reported from Bakhmut, Ukraine, and Shashank Bengali and Matthew Mpoke Bigg from London.

Pro-Russia war bloggers and commentators are celebrating the capture of Ukraine’s Luhansk region, with some seeing a sign that Russia’s momentum might accelerate. Others, however, are more skeptical, arguing that troops might be exhausted after weeks of intense fighting.

“The Ukrainian army has suffered a complete defeat,” commentator Yury Podolyaka declared on his Telegram channel, which has 2.2 million subscribers. In his daily video overview of the war, which he has claimed since the outset that Russia would win, he called for Russian forces to remain on the offensive after capturing the city of Lysychansk on Saturday.

“Today it is important to keep up the pace before the enemy has come to its senses, while it is still disheveled and hasn’t regrouped,” said Mr. Podolyaka, a native of Ukraine’s Sumy region. “We need to finish it up.”

Bloggers like Mr. Podolyaka have emerged as an influential group in Russia since the early days of the invasion in February, especially with independent reporting on the conflict in effect outlawed. Often using Telegram, a social messaging app, they have accumulated large numbers of subscribers with nationalistic but often critical commentary on the Russian war effort, especially in the early weeks, when its advances in Ukraine were stalled or repelled.

Igor Girkin, a retired Russian commander and one of the instigators of the separatist rebellion in eastern Ukraine in 2014, has criticized the Russian strategy in Luhansk in his posts.

The Russian troops, Mr. Girkin said, allowed most of the Ukrainian troops defending Lysychansk to escape. In other areas, the long battle for the Luhansk region gave the Ukrainians precious time to regroup and rearm in other areas, Mr. Girkin said. He also argued that Russia needs a larger army and must place its economy on a war footing in order to achieve its objectives in Ukraine.

“If we drag out general mobilization in Russia for longer, we can face a crisis in various areas of the Ukrainian front line,” he said, adding that Russian troops would not be able to fulfill the Kremlin’s objectives at their current levels.

Many pro-war bloggers agreed, however, that the Russian offensive in Ukraine must maintain ambitious goals. For Mr. Girkin, the only successful outcome would be if Russia captures most of Ukraine’s southeast and the government in Kyiv capitulates.

On Monday, President Vladimir V. Putin ordered that the troops involved in the Lysychansk offensive be given some rest to “increase their combat readiness,” while others should continue fighting. However, many bloggers said that the pause should not take too long, and that Russian forces should quickly train their sights on capturing the entire Donetsk, the province southwest of Luhansk.

“The main task today is to finish the enemy and advance toward Kramatorsk and Sloviansk,” Mr. Podolyaka said, referring two key cities in Donetsk.

In May, during a brief respite from the Russian rockets that had been hitting Kharkiv, Ukraine, Stanislav Drokin walked out of his jewelry atelier in his hometown’s city center to collect bomb fragments.

Mr. Drokin has lived in the atelier since Feb. 24, the day Russia invaded Ukraine. He moved there with his wife, Ludmila, along with two families of friends because it was too dangerous to remain at their home in Saltivka, a neighborhood in Kharkiv, Ukraine’s second-largest city.

Within a few weeks, however, everyone fled except for Mr. Drokin, who is 53 and, like all Ukrainian men from ages 18 to 60, is prohibited from leaving the country. (Ludmila joined the couple’s daughter, Alina, in Berlin, while the other families dispersed across Ukraine.)

For the first two months Mr. Drokin dedicated all his time to volunteering in the war effort. He allowed the atelier, which serves as both a production facility and showroom, to take on a third, de facto role: storage space for medicine and food.

Sorting and taking inventory of the supplies occupied most of his time. By mid-May, however, when the volunteer movement became more organized, Mr. Drokin was able to resume his jewelry practice.

Many members of the Ukrainian jewelry community — those who remain in the country and those in refuge abroad — said the war had motivated them to support Ukraine’s jewelry industry like never before.

What a difference a war makes.

Just a few months ago, Yandex stood out as a rare Russian business success story, having mushroomed from a small start-up into a tech colossus that not only dominated search and ride-hailing across Russia, but boasted a growing global reach.

A Yandex app could hail a taxi in far-flung cities like Abidjan, Ivory Coast; Oslo, Norway; or Tashkent, Uzbekistan; and the company delivered groceries in London, Paris and Tel Aviv. Fifty experimental Yandex robots trundled across the campus of Ohio State University in Columbus, bringing Grubhub food orders to students — with plans to expand to some 250 American campuses.

Often called “the coolest company in Russia,” Yandex employed more than 18,000 people; its founders were billionaires; and at its peak last November, it was worth more than $31 billion. Then President Vladimir V. Putin of Russia invaded Ukraine.

Almost overnight, as Western investors bolted from Russia and Western governments imposed harsh economic sanctions, its value dropped to less than $7 billion. The Nasdaq stock exchange suspended trading in its shares.

The sudden distaste for most things Russian prompted the company to shutter various international businesses, including the delivery services in London, Paris and Columbus.

Thousands of employees — nearly a sixth of the total — fled the country. Its founder, Arkady Volozh, and his top deputy stepped aside after the European Union sanctioned both, accusing them of abetting Kremlin disinformation.

The company is not facing insolvency. But its sudden change of fortune serves not just as a cautionary tale for investors in an authoritarian country dependent on the whims of a single ruler. Yandex is emblematic, too, of the problems Russian companies face in a radically changed economic landscape and of the growing divisions over the war in society at large.

The wife of Brittney Griner, the detained W.N.B.A. star who has been held in Russia since February, accused the White House on Tuesday of not doing enough to secure her release, a day after the basketball player sent a handwritten letter to President Biden asking him not to “forget about” her and other American detainees.

Cherelle Griner said she would no longer heed the government’s requests to let U.S. officials “handle this behind the scenes,” adding that she was concerned after Brittney Griner wrote her in a letter that she was physically “weak.”

“I will not be quiet anymore,” Cherelle Griner told “CBS Mornings.” “My wife is struggling and we have to help her.”

Cherelle Griner said on Tuesday that the family had still not received a reply from the president to Brittney Griner’s handwritten letter, calling it “very disheartening.” Karine Jean-Pierre, the White House press secretary, said Tuesday that Mr. Biden had read the letter.

In her letter to Mr. Biden, Brittney Griner urged the president to “do all you can to bring us home.”

“As I sit here in a Russian prison, alone with my thoughts and without the protection of my wife, family, friends, Olympic jersey or any accomplishments, I’m terrified I might be here forever,” she said in an excerpt from the letter shared by her representatives.

Brittney Griner, 31, was detained on Feb. 17 after she was accused of having hashish oil in her luggage at an airport near Moscow. She was in Russia to play with UMMC Yekaterinburg, a professional women’s basketball team for which she had competed during several W.N.B.A. off-seasons.

If she is convicted of the drug charges, Brittney Griner faces up to 10 years in a Russian penal colony. Her trial began Friday, and legal experts said that she was likely to be found guilty.

Although Brittney Griner has not yet responded to the charges, the U.S. government classifies her as “wrongfully detained,” meaning that it believes the charges against her are falsified — perhaps intended to pressure Washington over its involvement in Ukraine.

“The U.S. government continues to work aggressively — using every available means — to bring her home,” said Adrienne Watson, a spokeswoman for the National Security Council, in a statement on Monday.