As per Polish Deputy Interior Minister Pawel Szefernaker, over 450,000 people have entered Poland from Ukraine since a Russian invasion of the country started last Thursday.
He added that the number of people entering Poland fell slightly on Tuesday to 98,000 from a record number of over 100,000 on Monday.
Europe's largest refugee crisis this century
Approaching 680,000 people have fled Ukraine since the Russian military invasion on February 24, with the number rising rapidly.
"The number of people who have fled Ukraine to neighbouring countries has reached 677,000," Filippo Grandi, who heads the UN Refugee Agency (UNHCR), said on Twitter.
The UNHCR projected Tuesday that more than four million Ukrainian refugees may eventually need protection and assistance in neighbouring countries.
"We are looking at what could become Europe's largest refugee crisis this century," said Grandi.
The European Union's crisis management commissioner has said the figure could reach seven million.
More than 37 million people lived under the Kyiv government's control before last week's invasion.
A 60 hours wait for refuge
More than half of those who have fled Ukraine have crossed into Poland, with refugees waiting up to 60 hours to cross the border. Most arrivals are women and children from all parts of Ukraine.
Poland's border guards said Sunday that 90 percent of those arriving were being put up by friends or relations, but that reception centres were also being set up close to the frontier.
Poland was already home to 1.5 million Ukrainians before Russia invaded.
Poles are mobilising with offers of accommodation, money, clothes and work for the new arrivals.
The country's roads have been overwhelmed, making journeys longer and volunteers have set up checkpoints fearing Russian "provocations" and adding to bottlenecks.
Foreign students complain of racism
As the many foreign students in Ukraine -- from Africa, Asia and the Middle East attempt to reach safety, Jean-Jacques Kabeya is furious: like other he says has been stopped from leaving the country by its border guards.
He and several other foreigners alleged racist treatment by both the border guards and ordinary Ukrainians in interviews to AFP.
Two days after fleeing the bombing around the eastern city of Kharkiv, Kabeya reached the checkpoint at Shegyni, at the border with Poland, on Sunday evening.
But the soldiers and security guards there turned him back, said the 30-year-old student studying to become a pharmacist.
"They told me 'You're going to stay here, you're fleeing the war, stay here; you are going to fight with us -- you're not leaving, least of all you blacks'," he said.
Long lines at Poland border forcing people to turn to Romania
Some cars have now started moving in the opposite direction, with refugees from Ukraine were flocking into Romania to escape Russia's invasion -- and avoid massive jams at the Polish border.
"We thought about crossing through Poland but we heard that there was such a massive line and that people have been waiting for so long," tells one 30-year-old refugee.