(NewsNation Now) — More than 500,000 people have fled Ukraine since Russia invaded the country last week according to the U.N., and the mass exodus showed no signs of stopping Monday.

Shabia Mantoo, a UNHCR spokeswoman, said the latest and still growing count had 281,000 in Poland, more than 84,500 in Hungary, about 36,400 in Moldova, over 32,500 in Romania and about 30,000 in Slovakia. The rest were scattered in unidentified other countries, she said.

Long lines of cars and buses were backed up at checkpoints at the borders of Poland, Hungary, Slovakia, Romania and non-EU member Moldova. Others crossed the borders on foot, dragging their possessions away from the war and into the security of the EU.

Romania has said it could accept up to a half-million refugees, Hungary has said it is preparing for tens of thousands and Moldova has pledged to keep its borders open to Ukrainians.

Poland, which has welcomed large numbers of Ukrainian economic migrants in recent years, particularly after Russia’s incursions into Ukraine in 2014, made plans for weeks to accept refugees. Last month, the country said it was prepared to house at least one million refugees in hostels, dormitories and sporting facilities.

Poland, so far, has reported the most arrivals, with trains continuing to bring refugees into the border town of Przemysl on Monday. In winter coats to protect them against near-freezing temperatures, many carried small suitcases as they lined up at the platform to exit the station.

“We’ve talked to multiple families out here, every one of them has their own hellacious story. Some of these people have started in cities such as Kyiv, taking any means of transportation they could to get close to the border than walked another 30 miles to get to the border,” NewsNation’s Robert Sherman said live from the Ukraine-Poland border. “Once they got to the border, they had to stand in line waiting 24 to 48 hours just to get through and into Poland.”

Sherman said the refugees are still shocked that Russia invaded.

“They can’t believe this has happened. Two weeks ago they couldn’t believe this was going to happen and there’s still this sense of incredulous from a lot of the people who we speak with that they just can’t believe that this has happened to their country,” Sherman said.

U.S. intelligence agencies last week assessed that 1 million to 5 million Ukrainians could be displaced as Russian forces enter the country from the north, south and east.

“They’re tired, they’re cold, they’re hungry. They’re utterly exhausted and thankful to be here in Poland but still very worried about what’s happening in their beloved Ukraine,” Sherman said.

Poland is one of the easternmost members of NATO and the EU. Many Poles think membership in those organizations offers a good deal of protection from Russia as Russian President Vladimir Putin seeks to reassert Russia’s authority in a region that he believes should return to Moscow’s sphere of influence.

Hungary, another western border crossing for Ukrainians, has been openly hostile to refugees in the past, earning rebuke from the United Nations High Commissioner for Refugees (UNHCR).

Romania, the Czech Republic and Slovakia also received for refugees.

The Associated Press and the Hill contributed to this report.