The number of refugees fleeing the war in Ukraine has reached two million, the head of the UN refugee agency said Tuesday.

Filippo Grandi, the UN High Commissioner for Refugees, previously called the mas exodus from the country the fastest-growing refugee crisis in Europe since World War Two. 

"Today the outflow of reguess from Ukraine reaches two million people," he said on Twitter.

Earlier praised the "exemplary" welcome provided by Moldova, Poland and Romania, adding they seemed to be "coping" with the "natural spontaneous distribution."

Grandi stressed that the first waves of refugees after the February 24 invasion were those with "some resources."

"Many come by car, and especially they have connections. They can go where they have family, friends, communities," the commissioner said.

"It is possible that if the war continues... we will start seeing people that have no resources and no connections and that will be a more complex issue for European countries to manage going forward and there will need to be even more solidarity by everybody in Europe and beyond," he said.    

For comparison, Grandi said the Balkan wars in Bosnia and Kosovo saw "maybe two to three million people, but over a period of eight years." 

While other parts of the "world have seen this," Grandi added, "in Europe it's the first time since the Second World War."

On Monday, Grandi called it "the fastest growing refugee crisis in Europe since World War II," in a post to Twitter. 

After several failed attempts, Russia promised to open humanitarian corridors on Tuesday to allow civilians to flee the Ukrainian cities that have come under artillery fire.