The mass exodus of refugees from Ukraine to the eastern edge of the European Union showed no signs of stopping Monday, with the U.N. estimating more than 520,000 people have already escaped Russia’s burgeoning war against Ukraine.

Long lines of cars and buses were backed up at checkpoints at the borders of Poland, Hungary, Slovakia, Romania and non-EU member Moldova. Others crossed the borders on foot, dragging their possessions behind them.

U.N. High Commissioner for Refugees Filippo Grandi, speaking by video to the U.N. Security Council, said more than 520,000 refugees had fled Ukraine, a number he said “has been rising exponentially, hour after hour”.

The U.N. expects the total to reach 4 million in the coming weeks, Grandi said.