The Geneva-based UN High Commissioner for Refugees on Wednesday estimated the total number of refugees at 5.01 million.
More than half of the total, more than 2.8 million, first fled to Poland. While many have stayed there, an unknown number have traveled further. There are few border controls within the European Union.
UNHCR said on March 30 that 4 million people had fled Ukraine. The exodus has been slower in recent weeks than at the start of the war.
In addition to the refugees, the UN says more than 7 million people have been displaced in Ukraine.
Ukraine had a pre-war population of 44 million.