About 1.7 million Ukrainian refugees have crossed into neighboring countries in 11 days.
U.N. High Commissioner for Refugees Filippo Grandi said Sunday it is the fastest-growing refugee crisis in Europe since World War II.
Previously, the Syrian war was considered the largest global refugee crisis.
The UK has rejected opening its borders to Ukrainian refugees.
Ukraine’s Roma refugees say they were discriminated against by the Ukrainian border police en route to safety.
Last week, the African Union has criticized Ukrainian police for discriminating against Africans seeking to leave.
Moscow offered to set up humanitarian corridors from several bombarded Ukrainian cities Monday.
But Ukrainian leaders dismissed the offer, after learning some routes would lead refugees into Russia or Belarus.
Russian President Vladimir Putin said the war will continue until Ukraine accepts his demands and ends its resistance.
So far, international sanctions intended to punish Moscow have not slowed the invasion.