Some 2.5 million people have fled Ukraine since Russia invaded two weeks ago, and around two million more have been internally displaced by the "senseless" war, the United Nations said Friday.
The UN was planning for four million people to flee the country following the full-scale Russian invasion which began on February 24.
But it said it would be no surprise if that figure shot up, given the scale of the exodus.
UNHCR, the UN Refugee Agency, said 2,504,893 people had now fled Ukraine, with six in 10 of them now in neighboring Poland to the west.
"The number of refugees from Ukraine, tragically, has reached today 2.5 million," the agency's chief Filippo Grandi tweeted.
The UNHCR had been working on the estimate that four million people may eventually seek to leave Ukraine as the war continues.
But spokesman Matthew Saltmarsh said: "It is quite possible that that planning figure of four million will be revised up.
"We've just touched 2.5 million and that's in just over two weeks, so that really wouldn't be a surprise," he told reporters in Geneva, via video link from Poland, close to the Ukrainian border.
He said the rapid flow of refugees was "certainly unprecedented since World War II" in Europe.
"UNHCR commends the efforts of hosts and the immense solidarity shown by locals, volunteers and humanitarian organizations, who have been providing support for accommodation, transport, food, and financial and material donations," Saltmarsh said.
Paul Dillon, the spokesman for the UN's International Organization for Migration, said 116,000 of those who had fled Ukraine were third-country nationals.
Before Russia invaded, more than 37 million people lived in Ukrainian territory under the control of the Kyiv government.
More than 280,000 of those who have fled Ukraine have already made their way to other European countries, the UN said.
Russian strikes hit civilian targets in central Ukraine's Dnipro city on Friday, as Moscow's troops edged closer to the capital.
Kyiv mayor Vitali Klitschko said Thursday that half the city's 3.5 million population had fled and the capital "has been transformed into a fortress".
Freezing wait to cross
"UNHCR repeats its urgent call for the protection of civilians and civilian infrastructure, respect for international humanitarian law, and again thanks neighboring countries for keeping their borders open to those fleeing," Saltmarsh said.
He said the agency was working with the local authorities in border nations to improve the reception conditions at the frontier, where people wait in line for hours to cross, often in freezing temperatures.
The agency is working to provide heating points where especially vulnerable people, such as pregnant women, the elderly and the disabled, can sit and keep warm while they wait.
UNHCR is also rolling out an emergency cash program to tide refugees over.
And within Ukraine, Saltmarsh said the agency was ramping up its plans to help the millions of people forced to leave their homes.
"Core relief items for around 1.5 million people mobilized from UNHCR global stockpiles is in the pipeline," he said.