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.
In a statement, he said the operation in the rebel-held city was not going as quickly as hoped.
Separatists shot down two Ukrainian army helicopters, killing a pilot and a serviceman. Seven have been injured.
The UN Security Council met in emergency session at Russia's request.
Moscow's ambassador warned of "catastrophic consequences" if Kiev's military operation in eastern Ukraine continued, while the US called it "proportionate and reasonable".
Moscow came in for an onslaught of criticism from other nations which claimed it had sponsored the rebels and armed them with weapons capable of bringing down two Ukrainian helicopters, says the BBC's Nick Bryant in New York.
In his statement earlier, acting President 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.
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.
The self-proclaimed pro-Russia mayor of Sloviansk, Vyacheslav Ponomaryov, described the city has being "densely encircled".
"The shooting continues, then goes quiet, shots are heard on the streets, helicopters fly over the town now and again," he told Russia's Interfax news agency.
To the south, at least three people have been killed in clashes in the coastal city of Odessa between pro-Russian protesters and supporters of a unified Ukraine.
Gunfire was heard and stones and petrol bombs were thrown. A trade union building is on fire, with reports that pro-Russia activists barricaded themselves inside after their protest camp was burned down.
The West continues to accuse Moscow of provoking the unrest in eastern Ukraine, something Russia denies.
US President Barack Obama, at a meeting with German Chancellor Angela Merkel at the White House, warned of further sanctions against Russia if it did not "change course".
He said the idea that the unrest was caused by a "spontaneous uprising" was "belied" by the militants' use of missiles.
On the seven Organization for Security and Co-operation in Europe observers detained in Sloviansk by pro-Russian activists, Mr Obama said both leaders were "united in their outrage" about their treatment.
Elsewhere in eastern Ukraine:
- Unknown attackers seized a local railway control centre near Donetsk, disrupting train movement
- Pro-Russian rebels left the city council office and TV centre in the eastern Luhansk region
Eastern Ukraine has a large Russian-speaking population. It was a stronghold for President Viktor Yanukovych before he was overthrown by pro-Western protesters in February.
Russia then annexed the Crimean peninsula - part of Ukraine but with a Russian-speaking majority - in a move that provoked international outrage.
The crisis has plunged East-West relations to their lowest point since the Cold War ended in the early 1990s.