At the Sighetu Marmatiei crossing on Ukraine's border with Romania, women and children arrived by car, bicycle and on foot on Friday, clutching plastic bags and roll on suitcases as the snow fell.

One woman brushed away tears as she hugged a loved one waiting for her.

More than a week into the invasion, which Putin has called "a special military operation," over 1 million people have fled so far, in one of the fastest exoduses in memory, according to the United Nations.

Thousands more Ukrainians sought refuge in neighboring countries on Friday as the fighting back home intensified, receiving help from a groundswell of grassroots support from Central Europeans eager to help their Eastern neighbors.

Earlier in the day, Russian troops seized control of the largest nuclear power plant in Europe after a fierce battle, causing a fire in a building on the site that was later extinguished.

The United Nations' Office for the Coordination of Humanitarian Affairs said on Friday it had received no official written communication from Russia or Ukraine for assistance in setting up safe passage for civilians and supplies.

The two countries agreed on Thursday on the need for humanitarian corridors, however, to help civilians escape Moscow's eight-day-old invasion.

In Poland, some 800 orphans evacuated from Odessa, Kharkiv and other parts of Ukraine were expected to arrive later on Friday, in addition to 1,000 orphans already rescued, said the head of a Polish non-governmental organization helping to coordinate their evacuation.

"Places where they can be hosted in Poland are dispersed across the country, and the kids from one orphanage should not be separated from one another," Aleksander Kartasinski, the head of the Happy Kids NGO, told Reuters.

"I do my best to keep them together."

Polish bus operators have provided 17 vehicles that would ferry them for free, he said, in another sign of the fellow feeling in central Europe, where memories of Russian domination after World War Two run deep.

Some 73% of Poles were engaged in helping Ukrainians, mostly by donating food and hygiene products, according to a survey by pollster IQS for the Rzeczpospolita daily on Friday. Only 7% of those surveyed said they were not planning to help at all.

In Bulgaria, hotel owners on the Black Sea coast and small guesthouses throughout the country have offered free accommodation to Ukrainian refugees, while the state railway operator BDZ said they could travel in the country for free.