Human rights groups have documented what they say are brutal tactics by Russian forces in the city, depriving residents of water, food and medicine and forcing them to shelter in basements. Because cellphone communication has been cut off since early March, only incomplete reports of residents’ ordeal have filtered to the outside world. Two Associated Press journalists who had been in Mariupol detailed in a story Monday how they witnessed horrific scenes of children dying and homes and businesses being shelled; the journalists were rushed out after they said authorities told them the Russians were trying to hunt them down.

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As Mariupol residents continue to flee, a car carrying children came under fire, Oleksandr Starukh, governor of the nearby Zaporizhzhia region, said Monday. It was one of a series of incidents that he said left minors in serious condition. He said more than 20 buses were attempting to transit negotiated humanitarian corridors.

“Everything will have to be answered for. For every child. For every life,” Starukh said in a message on Telegram.

Addressing Ukrainians in a video address on Monday, President Volodymyr Zelensky praised the bravery of his people and condemned Russian troops, who are struggling to advance across different fronts, as “slaves of propaganda.”

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“During this invasion, heroes have constantly declared themselves among millions of our people. Once ordinary Ukrainians, and now fighters. Men and women who stand up for our state,” he said. “Stand up so that the enemy does not believe that this is a reality. But we will make them believe.”

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Zelensky, who has sought to both rally his people and to obtain greater foreign support, referenced an incident in which gunfire erupted during a protest of Russia’s capture of the southern city of Kherson, blaming Russian forces for the gunfire against residents. Video of the incident — which was verified by The Washington Post — showed a chaotic scene in which gunfire and explosions were heard and clouds of smoke appeared amid a group of demonstrators in Svobody Square.

“Kherson, hold on! We will never forget these shots,” Zelensky said.

In Kyiv, a massive explosion hit a shopping mall, killing at least eight people and providing further evidence of Russia’s intent to capture the capital city. American officials said Russian forces are stalled about nine miles to the northwest and about 18 miles to the east of Kyiv.

A U.S. defense official told reporters that Russia is now locked in a “near-desperate” attempt to accelerate its progress in Ukraine, having so far managed to seize only smaller cities such as Kherson, Berdyansk and Melitopol, instead of prizes such as Kharkiv, Mariupol and Kyiv.

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Facing logistical challenges and Ukrainian resistance, the official said, the Kremlin has resorted to using long-range shelling and missiles to bombard cities from a distance, making the war “much more dangerous for civilians.”

After a spate of initial attempts to broker safe passage for fleeing residents failed amid fighting, thousands of Ukrainians have been able to leave via humanitarian corridors. Ukrainian Deputy Prime Minister Iryna Vereshchuk said in a Telegram message that 8,000 people had been evacuated via such routes Monday, mostly from Kyiv and Mariupol.

But fleeing — like staying — remains a potentially perilous prospect for millions of families across the country. The war has unleashed an enormous wave of refugees, prompting 10 million people to flee their homes within Ukraine or to countries across Europe and beyond, the United Nations said this week. The figure amounts to a quarter of Ukraine’s prewar population.

More than 3 million people have crossed into neighboring countries, including more than 2 million to Poland alone, fueling concerns from Polish officials that local services and accommodations could soon be overwhelmed.

The constant flow has stretched the capacity of refugee centers and exhausted the ranks of Polish volunteers. Ukrainian refugees are lining up for hours to obtain the equivalent of a Social Security number so they can access Polish government services and find work.

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Warsaw Mayor Rafal Trzaskowski said 300,000 people had arrived in Warsaw in the past three weeks, around the same level that flowed into all of Europe each month during a refugee crisis in 2015. He said refugees needed to be distributed across the continent.

“We want to take everyone who needs help, but how many kids can we take into schools?” Trzaskowski said. “How can we do everything we can so the health system doesn’t break down in our city?”

In Russia, the government is holding more than 500 Ukrainian prisoners of war, the country’s human rights commissioner said Monday. Tatyana Moskalkova said the government was providing information about each captive to the International Committee of the Red Cross.

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“These are Ukrainian prisoners of war … that we are willing to exchange,” she said on the RT television channel.

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The fighting continued as President Biden held talks about the war with the leaders of France, Germany, Italy and Britain. The White House said the men “discussed their serious concerns about Russia’s brutal tactics in Ukraine, including its attacks on civilians,” along with diplomatic initiatives aimed at securing a pause in the fighting. Biden is scheduled to travel to Europe later this week to talk with NATO and other leaders.

While discussions between Russian and Ukrainian officials have so far failed to yield a breakthrough, global efforts to broker a negotiated settlement continue. Turkey’s government suggested this week that the two countries were getting closer to reaching a possible agreement that would include Ukraine’s “demilitarization” and Kyiv remaining out of NATO.

Even as Western nations continue to provide military aid, including Stinger and Javelin missiles and other weapons, they have rejected calls to establish a NATO-enforced no-fly zone over Ukraine, a move that alliance leaders say would probably result in war with Russia, a nuclear power.

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Andriy Yermak, the head of Ukraine’s presidential office, repeated Zelensky’s call for a no-fly zone and greater weaponry supplies on Monday, accusing some European countries of accepting a partial Russian occupation of Ukraine so they could continue buying energy from Russia.

“To freedom-loving people around the world we say: This is your war, too. Help us win it,” he wrote in a Washington Post opinion piece. He also wrote: “If we don’t get the equipment we need to succeed, [Russian President Vladimir] Putin won’t stop in Ukraine. He will go for NATO next.”

The war has triggered a sweeping global campaign of economic reprisal against Russia, sending the country’s economy into free-fall and isolating Putin as his government dismisses the prospect of compromising on its major objectives.

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It has also had intense diplomatic repercussions as Russia grows more isolated. On Monday, Russia’s Foreign Ministry said it had summoned Washington’s ambassador in Moscow, John Sullivan, to protest Biden’s description of Putin as a “war criminal.”

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“Such statements by the American president, unworthy of a statesman of such a high rank, put Russian-American relations on the verge of being severed,” the ministry said in a statement.

Addressing Russia’s complaint, State Department spokesman Ned Price said that it was “awfully rich to hear a country speak about inappropriate comments when that same country is engaged in mass slaughter.” Price said the Biden administration would continue to communicate with Russia when “necessary,” suggesting that Washington would not move first to sever ties with Russia.

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The White House on Monday renewed its warning about potential cyber incursions from the Kremlin, citing intelligence that the Russian government is exploring options for potential attacks.

Anne Neuberger, deputy national security adviser for cyber and emerging technologies, said that there wasn’t evidence of a specific attack, but that U.S. intelligence officials had detected “preparatory activity,” such as scanning websites and looking for potential vulnerabilities.

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Neuberger said the United States would respond to any actions taken by Russia. “We’re not looking for a conflict with Russia,” she said. “If Russia initiates a cyberattack against the United States, we will respond.”

As the conflict continues, Ukrainians’ support appears to be growing for continuing the fight, a new poll showed. The survey by Kyiv-based Info Sapiens found that 91 percent of Ukrainians now believe their country can repel Russia’s assault, up from 56 percent before Putin’s invasion.

Rosenzweig-Ziff reported from Warsaw. Ryan and Nakashima reported from Washington. Loveday Morris in Dnipro, Ukraine; Mary Ilyushina in Riga; Latvia; Ellen Francis in London; and Karoun Demirjian, John Hudson, Harry Stevens, Reis Thebault and Matt Viser in Washington contributed to this report.