Thursday's invasion followed weeks of escalating tensions, as Russia massed troops along Ukraine's borders.
The UK, EU and other Western allies have vowed to impose tough new sanctions to punish Moscow, but say they will not send in troops.
"These are among the darkest hours of Europe since the Second World War," EU foreign affairs chief Josep Borrell said.
Dozens of people have been killed, including about 10 civilians. Six died in an air strike in Brovary near the capital Kyiv. A man was also killed in shelling outside the major north-eastern city of Kharkiv.
A Ukrainian presidential adviser said that more than 40 soldiers had died and many more were wounded. Ukraine said it had killed 50 Russian troops and shot down six Russian aircraft, but this has not been verified.