A woman with children arrives at a temporary accommodation in Poland. (R) A mother holds her baby on board of a bus after crossing from Ukraine into Poland at the Medyka border. Reuters / AFP
UNHCR, the UN refugee agency, said 3,270,662 people had joined the exodus since the war began on Feb.24, or another 100,765 since Thursday's update.
"We have seen a general slowdown" in flow since the early days of the conflict, said UNHCR spokesman Matthew Saltmarsh.
As for people still within Ukraine who have left their homes, "It's safe to assume the number is considerably higher than two million," he said.
However, "the pace and magnitude of the internal displacement and refugee exodus from Ukraine, as well as resulting humanitarian needs, will only increase if the situation deteriorates."
Some 90 per cent of those who have fled are women and children, he added. Ukrainian men aged 18 to 60 are eligible for military call-up and cannot leave.
The UN's International Organisation for Migration said that as of Wednesday, 162,000 third-country nationals had fled the country.
A border guard checks the documents of Ukrainian refugees.
The UNHCR initially estimated that up to four million people could leave Ukraine, but last week admitted that figure might well be revised upwards.
Before the conflict, Ukraine had a population of 37 million in the regions under government control, excluding Russia-annexed Crimea and the pro-Russian separatist regions in the east.
Here is a breakdown of where Ukrainian refugees headed to, according to UNHCR:
Poland — Six in every 10 Ukrainian refugees crossed the Polish border, or 1,975,449 people so far, according to the UNHCR's latest figures. But Poland's border guards said on Friday, the total number of refugees crossing from Ukraine had exceeded two million.
Tens of thousands of people are also entering Ukraine from Poland — mostly those returning to fight but also others seeking to care for elderly relatives or to bring their families out to Poland.
Refugees take at a border checkpoint in Kroscienko, Poland. Reuters
The data of arrivals into Ukraine's neighbouring countries, which are in Europe's Schengen open-borders zone — Poland, Hungary and Slovakia — only represent border crossings into that country.
"We estimate that a large number of people have moved onwards to other countries," UNHCR said.
Romania — The UNHCR said more than half a million people had now made their way into Romania.
Some 508,692 have reached the country, including people who had crossed over from Moldova to reach the EU member state.
A Ukrainian family from Lviv makes their way to cross the border from Poland to Ukraine. Reuters
The UNHCR figures per neighbouring country are 281,563 higher than their overall total — a difference, which the agency says reflects the number of people who crossed between Moldova and Romania.
The vast majority are thought to have made their way onto other countries further into Europe.
Moldova — The UNHCR said 355,426 Ukrainians had crossed into the non-EU state wedged between Romania and Ukraine. It is the closest border to the major port city of Odessa.
Many Ukrainians fleeing the fighting transit through Moldova, a small nation of 2.6 million people and one of the poorest in Europe, en route westwards to Romania and other countries beyond.
Hungary — Ukrainian refugees who have crossed into Hungary number 291,230.
Hungary has five border posts with Ukraine and several frontier towns, including Zahony, where local authorities have turned public buildings into emergency centres for refugees.
Slovakia — A total of 234,738 refugees made it across Ukraine's shortest border into Slovakia. Another 5,894 Ukrainians entered Slovakia on Thursday.
Russia — Some 184,563 refugees have sought shelter in Russia.
In addition, UNHCR said 50,000 people had crossed into Russia from the pro-Russian Donetsk and Lugansk regions of eastern Ukraine between February 21 and 23.
Belarus — And 2,127 refugees have made it to Belarus, the UNHCR says.Agence France-Presse
Fighting raged near Kyiv on Saturday and heavy shelling in other areas threatened new attempts to evacuate trapped civilians as France said Russian President Vladimir Putin showed no readiness to end the war in Ukraine.
Separately, US Deputy Secretary of State Wendy Sherman said Russia was showing signs of willingness to engage in substantive negotiations about ending a conflict in which thousands have died. More than 2.5 million people have fled.
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