That movement of mostly women and children is coming at a faster rate than the relocation of people at the height of the Balkan wars in the 1990s, and far faster than the one during the Hungarian refugee crisis of 1956, said Filippo Grandi, the United Nations High Commissioner for Refugees.
Most refugees are fleeing west into Poland, Slovakia, Hungary, Romania and Moldova, which have all opened their borders to Ukranians looking to escape the conflict.
More than 650,000 have already arrived in Poland, which has absorbed the most people, and between 50,000 and 80,000 continue to arrive there each day.
Polish aid organisations at the border claim their capacity is being stretched to breaking point.