[npr_image:1084117346] Updated March 3, 2022 at 5:28 AM ET

The number of refugees fleeing across the borders of Ukraine has reached a grim milestone, the U.N. said, as Russia's siege of key cities across the country extended into Thursday, with Moscow saying it now controls a city in southern Ukraine.

The U.N.'s top refugee official said on Wednesday that 1 million people have now fled across the borders of Ukraine since Russian forces invaded a week ago.

"In just seven days we have witnessed the exodus of one million refugees from Ukraine to neighbouring countries," U.N. High Commissioner for Refugees Filippo Grandi wrote in a tweet on Wednesday.

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The new total of refugees from Ukraine amounts to a little more than 2% of the country's total population of 44 million. According to the United Nations High Commissioner for Refugees (UNHCR), around half of the refugees are in Poland, with Hungary, Moldova and Slovakia being the other top destinations, while others have fled to various other European countries.

Grandi added in his tweet: "For many millions more, inside Ukraine, it's time for guns to fall silent, so that life-saving humanitarian assistance can be provided."

News of the refugee milestone came as Russian forces appeared to seize their first major city.

"The occupiers are moving through the streets in heavy machinery," said the spokesperson for the mayor of Kherson, a strategic port city on the Dnieper River near the Black Sea. The mayor met with Russian forces and asked the Russians "not to shoot at houses and civilians, because we already have several hundred dead."

When NPR spoke with the representative, the Ukrainian flag still few over city hall, but a Russian Defense Ministry spokesperson tells the AP that Kherson is under "complete control" of the Russian forces.

"I see the Russian military on my street," Kherson resident Yevhenia Revenko told NPR's Lauren Frayer as she was wandering Kherson's streets in search of an open store to buy food. "But I can't find any. We try to find food because we're sitting at home for three days without permission to go out. So now, they give us some time – at least a couple of hours – to find food."

Revenko, a 25-year-old doctoral student, said there are tanks in the city snipers on rooftops. On Wednesday, a senior U.S. Defense official told NPR that Kherson was "very much contested" at that point.

Separately on Wednesday, the United Nations General Assembly approved a nonbinding resolution condemning Russia for invading Ukraine and demanding that it withdraw its military forces.

Wednesday's vote follows after a series of speeches during which the majority of countries called on Russia to end the violence in Ukraine. The ongoing violence has continued for a week.

The resolution passed overwhelmingly by a vote of 141-5 with 35 abstentions. The five countries that voted against it were Russia, Belarus, Syria, North Korea and Eritrea.

"The truth is that this war was one man's choice and one man alone: President Putin," said U.S. Ambassador to the U.N. Linda Thomas-Greenfield. "It was his choice to force hundreds of thousands of people to stuff their lives into backpacks and flee the country."

"Those were President Putin's choices," she added. "Now it is time to make ours. The United States is choosing to stand with the Ukrainian people."

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