Ukraine's government troops have now sealed off Sloviansk, reports say
Many pro-Russia rebels have been killed, injured and arrested in the Ukrainian government offensive in the eastern city of Sloviansk, acting President Oleksandr Turchynov has said.
But, in a statement, he said the operation in the rebel-held city was not going as quickly as hoped.
Rebels earlier shot down two Ukrainian army helicopters, killing a pilot and a serviceman.
Russia has called for an emergency meeting of the UN Security Council.
Moscow has said the use of the Ukrainian army against its own people is "leading Ukraine to catastrophe" and said the Security Council meeting should take place on Friday.
The situation in Sloviansk remains unclear, with Kiev earlier saying that half the city was "under control" of Ukrainian units.
Mr Turchynov said the fight against rebel forces was "greatly complicated" by the fact that the conflict in eastern Ukraine was taking place in population centres.
Two Ukrainian army service personnel were killed in the fight for Sloviansk, he said, and he accused pro-Russian forces of hiding behind civilians and hostages.
All pro-Russian checkpoints around the city had been captured, Mr Turchynov added, though separatists have spoken of several still being under their control.
Local people could be seen standing in front of Ukrainian tanks, according to Paul Ronzheimer, a reporter with Germany's Bild newspaper in the city.
Many told the soldiers to retreat, exclaiming "shoot us, we are separatists as well, just because we want to belong to Russia, shoot us", Mr Ronzheimer said.
The BBC's Fergal Keane, at a bridge outside Sloviansk where there is a stand-off between Ukrainian troops and pro-Russian locals, describes the atmosphere as tense and unpredictable.
To the south, there were clashes in the coastal city of Odessa between pro-Russian protesters and supporters of the Kiev government.
At least one person has been killed amid reports of gunfire.
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