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At least 677,000 people have fled Ukraine to neighboring countries after Russian forces invaded last week, leading to what the United Nations says could be "Europe’s largest refugee crisis this century."

Long lines of buses and cars have been backed up at the borders of Poland, Hungary, Moldova, Romania, and other countries as the mass exodus showed no signs of slowing down on Tuesday. 

In Poland, refugees had to wait for up to 60 hours in freezing temperatures before crossing the border. There was a 20-hour line to get into Romania. 

An Ukrainian mother cries after crossing to Poland as first migrants from Ukraine enter Poland after Russia bombarded Ukrainian territory.

An Ukrainian mother cries after crossing to Poland as first migrants from Ukraine enter Poland after Russia bombarded Ukrainian territory. (Photo by Dominika Zarzycka/NurPhoto)

Despite the long waits, the UN commended Ukraine's neighbors for opening their borders and accommodating those who are fleeing the war. 

"The challenge to admit and register, to meet the needs and ensure the protection of those fleeing, are daunting, but so far they have been met, though I am seriously concerned about the likely, and further escalation in the number of arrivals," Filippo Grandi, the United Nations High Commissioner for Refugees, said about the crisis. 

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Joel Colon, an American missionary who has lived in Ukraine since 2005, told Fox News Digital that he saw people fleeing Kyiv on foot when he was leaving the city last Thursday. 

Hundreds of beds are placed inside a sports hall to accommodate Ukrainian refugees fleeing Russian invasion at the border crossing town of Medyka, Poland, on Tuesday, March 1, 2022. 

Hundreds of beds are placed inside a sports hall to accommodate Ukrainian refugees fleeing Russian invasion at the border crossing town of Medyka, Poland, on Tuesday, March 1, 2022.  ((AP Photo/Visar Kryeziu))

Up to four million refugees may seek refuge in neighboring European countries in the coming days and weeks if the conflict continues, Grandi said. 

While many of the refugees are Ukrainian citizens, there are also citizens of more than 100 nationalities who live in Ukraine and are now trying to escape Russia's invasion, including Uzbeks, Nigerians, Moroccans, Afghans, Iranians, Iraqis, and others, Polish U.N. Ambassador Krzysztof Szczerski said. 

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The President of Nigeria condemned reports that some Nigerian students were turned away from the Polish border, saying on Saturday that "all who flee a conflict situation have the same right to safe passage under UN Convention and the [color] of their passport or their skin should make no difference." 

Refugees fleeing war in Ukraine wait to board a bus as they arrive to Palanca, Moldova, Tuesday, March 1, 2022. 

Refugees fleeing war in Ukraine wait to board a bus as they arrive to Palanca, Moldova, Tuesday, March 1, 2022.  (AP Photo/Aurel Obreja)

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Most of the refugees are women and children, as men between the ages of 18 and 60 have been banned from leaving Ukraine. 

Grandi, the UN official, appealed to donors on Tuesday, saying that $1.7 billion is needed to support refugees as well as people affected by the war who are still in Ukraine. 

The Associated Press contributed to this report.