The Interior Mnistry said on Thursday that the pro-Russian rebels were killed as paratroopers took over three "illegal checkpoints" around the town, which has been in separatist control for almost two weeks.
Videos posted online showed smoke rising from barricades around the town. Reports said that rebels had set fire to the barricades as they abandoned them and retreated from Ukranian forces.
Reuters reported that Ukrainian troops had set up new positions around the town.
The AFP agency said that Ukrainian forces had told pro-Russian rebels to leave government buildings they were occupying, although this was not confirmed by any other source.
Russia condemned any such operations, with President Vladimir Putin saying on Thursday that there would be consequences if the Ukraine army was used against pro-Russian activists.
He said any such action was "just a punitive operation and it will of course incur consequences for the people making these decisions, including (an effect) on our interstate relations".
The operation came hours after the government reported that its forces had taken control of the town hall in the city of Mariupol, and repelled an attack on an army base in the eastern town of Artemivsk, the ministries said.
Separatist sources also reported the loss of the town hall in Mariupol. The city was the scene of a rebel attack on troops last week that left three rebels dead. The separatists had held the town hall since April 13.