President Biden on Saturday said the United States understands Poland's decision to take in more than 2 million Ukrainian refugees amid Russia's invasion because "thousands of people a day, literally," are crossing the U.S. southern border.

Biden made the remarks during a meeting with Polish President Andrzej Duda in Warsaw to discuss Russian President Vladimir Putin's ongoing war in Ukraine.

"We do acknowledge that Poland is taking on a significant responsibility that I don't think should just be Poland and should be the whole world — all of NATO's responsibility," Biden said. "The fact that you have so many Ukrainians seeking refuge in and in … Poland — we understand that because we have on our southern border thousands of people a day literally, not figuratively, trying to get to the United States."

U.S. President Joe Biden, left, and Polish President Andrzej Duda shake hands during a military welcome ceremony at the Presidential Palace in Warsaw, Poland, on Saturday, March 26, 2022. (AP Photo/Czarek Sokolowski)

U.S. President Joe Biden, center, and Polish President Andrzej Duda walk past honour guard during a military welcome ceremony at the Presidential Palace in Warsaw, Poland, on Saturday, March 26, 2022. (AP Photo/Czarek Sokolowski)

President Joe Biden meets with Polish President Andrzej Duda at the Presidential Palace, Saturday, March 26, 2022, in Warsaw. (AP Photo/Evan Vucci)

He added that the United States believes it should do its part "relative to Ukraine, as well, by opening our borders to another hundred thousand people."

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More than 2.2 million Ukrainians have fled to Poland to escape Russian fire.

Axana Opalenko, 42, holds Meron, 2 months old, in an effort to warm him after fleeing from Ukraine, at the border crossing in Medyka, Poland. (AP Photo/Visar Kryeziu)

The White House announced Thursday that the U.S. will welcome up to 100,000 Ukrainian refugees using multiple methods including the refugee admissions program, as well as parole and immigrant and non-immigrant visas. The White House also announced that the U.S. will impose new sanctions on Russian individuals and companies.

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Administration officials said that President Biden's cap of 125,000 refugees for Fiscal Year 2022 remains in effect, but that those who enter via processes other than the refugee program will not count toward that total.

People surround a car as it arrives carrying food donations at a makeshift camp for migrants seeking asylum in the United States at the border crossing Friday, March 12, 2021, in Tijuana, Mexico. (AP Photo/Gregory Bull)

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In February alone, there were 164,973 encounters at the U.S. southern border, compared to 101,099 encounters in February 2021 — a month that preceded a massive surge in numbers in the spring and summer months that overwhelmed U.S. Border Patrol and led to migrants quickly being released into the interior. In February 2020, there were just 36,687 encounters.

The Washington Post reported this week that preliminary Customs and Border Protection (CBP) data indicates that authorities are on track to have encountered more than 200,000 in March, compared to 173,277 in March last year.

Fox News' Ronn Blitzer and Adam Shaw contributed to this report.