Ukrainians who could escape have spilled into neighboring Poland, Romania, Slovakia, and elsewhere, while tens of thousands of people have been internally displaced. The United Nations refugee agency estimated that the number of the refugees could swell to 4 million by July.

While visiting Ukrainian refugees on the Polish border over the weekend, U.S. Secretary of State Antony Blinken said Washington was seeking $2.75 billion for the unfolding humanitarian crisis.

It comes as the Ukrainian military said on March 6 that it was engaged in "fierce battles" with Russian forces for the control of borders at the southern city of Mykolayiv and Chernihiv in the north.

"The main efforts are focused on defending the city of Mariupol," the military said in Facebook post. An operation by Ukrainian forces was also under way in the Donetsk region, it added.

Ukraine's military also claimed that it had shot down 88 Russian aircraft so far and captured some pilots.

Mariupol has for days been under siege and without electricity, food, and water. After Russia declared a cease-fire to open a humanitarian corridor, local officials said the population of 450,000 could begin to leave the city by bus and private cars.

But the evacuation has been delayed, with officials saying that “the Russian side is not adhering to the cease-fire and has continued shelling both Mariupol itself and its environs.”

In a televised address late on March 5, Ukrainian President Volodymyr Zelenskiy called on people in areas occupied by Russian troops to fight.

"We must go outside and drive this evil out of our cities," Zelenskiy said, vowing to rebuild his nation.

Based on reporting by Reuters and AFP