GENEVA — The number of refugees fleeing Ukraine reached 2 million on Tuesday, according to the United Nations, the fastest exodus Europe has seen since World War II.

“Today the outflow of refugees from Ukraine reaches two million people. Two million,” Filippo Grandi, the UN High Commissioner for Refugees, wrote on Twitter.

The update came as a new effort to evacuate civilians along safe corridors finally got underway Tuesday. The route out of the eastern city of Sumy was one of five promised by the Russians to offer civilians a way to escape the Russian onslaught.