The number of refugees fleeing Ukraine since February 24 climbed to more than 2.8 million, United Nations data showed on Monday, in what has become Europe's fastest-growing refugee crisis since World War Two.
European Union officials have said 5.0 million may end up fleeing while others have put the figure higher due to the Russia-Ukraine war, reports Reuters.
Millions of people have also been displaced inside Ukraine, with many evacuated only as far as the quieter western regions, including to cities like Lviv.
Myroslava, 52, fled her home in the Ternopil region, in western Ukraine, and was waiting in a terminal of Krakow station in Poland to be picked up by acquaintances. She did not know where she would stay.
"We left because of the attack yesterday," she said, adding that she had hoped western Ukraine would be safe. "We weren't planning to leave, but as it was so close we decided to."
Polish Prime Minister Mateusz Morawiecki told a news conference with his counterparts from Ukraine and Lithuania that the attack near its border showed Russia wanted to "create panic among the civilian population".
Mira from Kyiv, travelling with her mother to Warsaw, said she had been surprised by the Russian attack near Lviv. "I just panicked and felt scared," she said.