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.
More than half of those who have fled Ukraine have crossed into Poland.
The UNHCR said Tuesday that 377,400 people had done so, 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.
Some 89,561 people have so far crossed from Ukraine into Hungary, the UNHCR said.
Several border towns such as Zahony have set up public buildings as reception centres, with ordinary people donating food and clothes, the interior ministry said.
Arrivals are steady and waiting times vary, with ordinary Hungarians, local authorities and humanitarian agencies providing help.
UNHCR said 65,391 people had fled Ukraine and were now in Moldova.
It is taking 24 hours to cover the 60 kilometres between the Ukrainian major port city of Odessa and the Moldovan border.
An airlift from Dubai is due to arrive on Wednesday bringing more emergency supplies for refugees.
The UNHCR said 54,304 had fled across Ukraine’s shortest border to Slovakia.
“The government is maintaining an open and welcoming policy towards refugees, and has rapidly changed asylum laws to help fast-track asylum procedures,” said the agency.
The UN Refugee Agency said 38,461 people who fled were now in Romania.
There are queues of up to 20 hours to cross the border.
“Local communities are generously helping with transport and accommodation, while private companies are paying for hotels,” the UNHCR said.
Many people are passing through Siret in the north, where a camp has been set up, along with a second site near Marmatiei.
Romanians have taken to social media to organise donations of food and clothing.
More than 300 people had crossed from Ukraine into Belarus, the UNHCR said.
Grandi said a number of people had moved from eastern Ukraine into Russia.
The UNHCR does not have figures for the numbers of people who have crossed Ukraine’s longest border, though it is thought to be significant.
The UN Refugee Agency said Tuesday that around 51,800 of those who had fled Ukraine into neighbouring countries had already moved onwards towards other European states.
Grandi said refugees would head for established Ukrainian communities in other countries, with several thousand already in the Czech Republic.
Karolina Lindholm Billing, the UNHCR representative to Ukraine, estimated that a million people had been internally displaced by the Russian invasion.
She cautioned that the agency still did not have reliable figures.