KYIV, Ukraine >> More than 1 million people have fled Ukraine following Russia’s invasion, in the swiftest refugee exodus this century, the United Nations said Thursday, as Russian forces kept up their bombardment of the country’s second-biggest city, Kharkiv, and laid siege to two strategic seaports.

The tally the U.N. refugee agency released to The Associated Press was reached Wednesday and amounts to more than 2% of Ukraine’s population being forced out of the country in less than a week. The mass evacuation could be seen in Kharkiv, where residents desperate to escape falling shells and bombs crowded the city’s train station and pressed onto trains, not always knowing where they were headed.

Overnight, Associated Press reporters in Kyiv heard at least one explosion before videos started circulating of apparent strikes on the capital. The targets were not immediately clear.

A statement from the general staff of Ukraine’s armed forces didn’t address the strikes, saying only that Russian forces were “regrouping” and “trying to reach the northern outskirts” of the city.

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“The advance on Kyiv has been rather not very organized and now they’re more or less stuck,” said military analyst Pavel Felgenhauer told the AP in Moscow.

In a videotaped address, Ukrainian President Volodymyr Zelenskyy called on Ukrainians to keep up the resistance. He vowed that the invaders would have “not one quiet moment” and described Russian soldiers as “confused children who have been used.”

Moscow’s isolation deepened when most of the world lined up against it at the United Nations to demand it withdraw from Ukraine. And the prosecutor for the International Criminal Court opened an investigation into possible war crimes.

Felgenhauer said with the Russian economy already suffering, there could be a “serious internal political crisis” if Russian President Vladimir Putin does not find a way to end the war quickly.

“There’s no real money to run to fight this war,” he said, adding that if Putin and the military “are unable to wrap up this campaign very swiftly and victoriously, they’re in a pickle.”

With fighting going on on multiple fronts across Ukraine, Britain’s Defense Ministry said Mariupol, a large city on the Azov Sea, was encircled by Russian forces, while the status of another vital port, Kherson, a Black Sea shipbuilding city of 280,000, remained unclear.

Ukraine’s military said Russian forces “did not achieve the main goal of capturing Mariupol” in its statement, which did not mention Kherson.

Putin’s forces claimed to have taken complete control of Kherson, which would be the biggest city to fall yet in the invasion. A senior U.S. defense official disputed that.

“Our view is that Kherson is very much a contested city,” the official said, speaking on condition of anonymity.

Zelenskyy’s office told the AP that it could not comment on the situation in Kherson while the fighting was still going on.

The mayor of Kherson, Igor Kolykhaev, said Russian soldiers were in the city and came to the city administration building. He said he asked them not to shoot civilians and to allow crews to gather up the bodies from the streets.

“We don’t have any Ukrainian forces in the city, only civilians and people here who want to LIVE,” he said in a statement later posted on Facebook.

The mayor said Kherson would maintain a strict 8 p.m.-to-6 a.m. curfew and restrict traffic into the city to food and medicine deliveries. The city will also require pedestrians to walk in groups no larger than two, obey commands to stop and not to “provoke the troops.”

“The flag flying over us is Ukrainian,” he wrote. “And for it to stay that way, these demands must be observed.”

Mariupol Mayor Vadym Boychenko said the attacks there had been relentless.

“We cannot even take the wounded from the streets, from houses and apartments today, since the shelling does not stop,” he was quoted by the Interfax news agency as saying.

Russia reported its military casualties for the first time in the war, saying nearly 500 of its troops have been killed and almost 1,600 wounded. Ukraine did not disclose its own military losses but said more than 2,000 civilians have died, a claim that could not be independently verified.

In a video address to the nation early Thursday, Zelenskyy praised his country’s resistance.

“We are a people who in a week have destroyed the plans of the enemy,” he said. “They will have no peace here. They will have no food. They will have here not one quiet moment.”

He said the fighting is taking a toll on the morale of Russian soldiers, who “go into grocery stores and try to find something to eat.”

“These are not warriors of a superpower,” he said. “These are confused children who have been used.”

Meanwhile, the senior U.S. defense official said an immense Russian column of hundreds of tanks and other vehicles appeared to be stalled roughly 25 kilometers (16 miles) from Kyiv and had made no real progress in the last couple of days.

The convoy, which earlier in the week had seemed poised to launch an assault on the capital, has been plagued with fuel and food shortages, the official said.

On the far edges of Kyiv, volunteers well into their 60s manned a checkpoint to try to block the Russian advance.

“In my old age, I had to take up arms,” said Andrey Goncharuk, 68. He said the fighters needed more weapons, but “we’ll kill the enemy and take their weapons.”

Around Ukraine, others crowded into train stations, carrying children wrapped in blankets and dragging wheeled suitcases into new lives as refugees.

In an email, U.N. refugee agency spokesperson Joung-ah Ghedini-Williams told the AP that the refugee count surpassed 1 million as of midnight in central Europe, based on figures collected by national authorities.

Shabia Mantoo, another spokesperson for the agency, said that “at this rate” the exodus from Ukraine could make it the source of “the biggest refugee crisis this century.”

Russian forces pounded Kharkiv, Ukraine’s biggest city after Kyiv, with about 1.5 million people, in another round of aerial attacks that shattered buildings and lit up the skyline with flames. At least 21 people were killed over the past day, said Oleg Sinehubov, head of the Kharkiv regional administration.

Several Russian planes were shot down over Kharkiv, according to Oleksiy Arestovich, a top adviser to Zelenskyy.

“Kharkiv today is the Stalingrad of the 21st century,” Arestovich said, invoking what is considered one of the most heroic episodes in Russian history, the five-month defense of the city from the Nazis during World War II.

From his basement bunker, Kharkiv Mayor Igor Terekhov told the BBC: “The city is united and we shall stand fast.”

Russian attacks, many with missiles, blew the roof off Kharkiv’s five-story regional police building and set the top floor on fire, and also hit the intelligence headquarters and a university building, according to officials and videos and photos released by Ukraine’s State Emergency Service. Officials said residential buildings were also hit, but gave no details.