The UNHCR estimated in a March 1 report that more than 4 million people could flee Ukraine if the war grinds on. On Tuesday the agency said it may soon need to increase that forecast.
Millions of people have also been on the move within Ukraine to flee fighting. The United Nations Office for the Coordination of Humanitarian Affairs estimated on Feb. 27 that within two months there would be 7.5 million internally displaced people.
WILL REFUGEES STAY IN NEIGHBOURING NATIONS?
Ukrainians can travel to the European Union without a visa for up to 90 days, giving them an immediate pathway to refuge. Ukraine borders four EU member states - Poland, Slovakia, Hungary and Romania.
Thanks to the Schengen Treaty, when you reach one EU nation, you can travel freely around most of the bloc, and many Ukrainians have already moved on to member states further away.
Some 80,035 Ukrainian refugees were registered in Germany as of Wednesday, while some 23,872 Ukrainians have reached Italy since the start of the crisis.
The EU has said it will grant Ukrainian refugees the right to stay and work in the bloc for up to three years.
As of June 2020, some 6.1 million Ukrainians already lived abroad, and many of the refugees are expected to try to reach their expat relatives wherever they might be.
HOW EASY IS IT TO MOVE BEYOND THE EUROPEAN UNION?
It can prove complicated.
Britain established two visa schemes for Ukrainians seeking sanctuary, but it is a bureaucratic, time-consuming process and as of Wednesday only around 700 visas had been issued. Prime Minister Boris Johnson has defended the process, saying Britain needs to carry out security checks on refugees.
The United States said last week it would offer temporary protected status to Ukrainians already inside the country. White House Press Secretary Jen Psaki said last month that while the United States was prepared to accept more refugees "most, if not the majority" of them would prefer to stay in Europe.
Israel said on Tuesday it was ready to take in just 5,000 Ukrainians and allow 20,000 others who had arrived before the Russian invasion to remain temporarily.