Hundreds of thousands of refugees have fled Ukraine for neighboring European countries as the third day of Russia’s full-scale invasion intensifies with fighting in the capital Kyiv.

The conflict has already driven nearly 120,000 Ukrainians from their homes and across its borders to Poland, Moldova, Hungary, Romania and Slovakia, the United Nations refugee agency said Saturday.

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"Almost 116,000 have crossed international borders as of right now. This may go up, it’s changing every minute," said Shabia Mantoo, the spokeswoman of the U.N. High Commissioner for Refugees. "It’s very fluid and changing by the hour."

Ukrainians leaving Ukraine to Poland

A border guard assists refugees from Ukraine as they arrive at the Korczowa border crossing, Poland, Saturday, Feb. 26, 2022. (AP Photo/Czarek Sokolowski)

Mantoo added that some refugees have even fled into Belarus, where some Russian troops were stationed before entering Ukraine days earlier.

The U.N. estimates that up to 4 million people could flee Ukraine if the fighting with Russian forces escalates. 

While Mantoo didn't immediately provide the refugee numbers by country, Poland's government said Saturday morning that more than 100,000 Ukrainians had crossed the Polish-Ukrainian border in the past 48 hours.

Refugees in Ukraine that fled to Poland

Refugees who fled the conflict from neighboring Ukraine rest in a school building in Przemysl, Poland, Saturday, Feb. 26, 2022. (AP Photo/Petr David Josek)

Refugees at Poland's Medyka border crossing said a line of thousands of Ukrainians waiting to enter Poland stretched 9 miles (15 kilometers) into Ukraine, Polish broadcaster TVN24 reported.

"I arrived today at 3 a.m. and I am waiting for my wife," Taras, 25, told Reuters from Poland's side of the crossing. "She called me from the Ukrainian side and there is a 30-kilometer queue of cars and people. She said she does not know when she will cross."

Ukrainians leaving Ukraine after Russia invaded

Refugees from Ukraine arrive at the Korczowa border crossing, Poland, Saturday, Feb. 26, 2022. (AP Photo/Czarek Sokolowski)

Refugees arriving in the Hungarian border town of Zahony said men of fighting age were not being allowed to leave Ukraine.

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As Ukrainian forces and citizens continued to repel Russia’s advance on Kyiv early Saturday, Ukraine’s President Volodymyr Zelenskyy refused a U.S. offer to evacuate and vowed to stay in the capital.

"The fight is here," Zelenskyy said in a video update filmed on his phone.

The Associated Press contributed to this report.