People fleeing what had been the relative safety of western Ukraine joined thousands crossing into eastern Europe on Monday after Russia attacked a Ukrainian base near the border with NATO-member Poland.
Ukraine said 35 people were killed at the base on Sunday. Moscow said up to 180 "foreign mercenaries" died and a large number of foreign weapons were destroyed.
Ukraine also reported renewed air strikes on an airport in the west of the country.
The number of refugees fleeing Ukraine since Russia invaded on Feb. 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 million may end up fleeing while others have put the figure higher.
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.
