Pro-Russian rebels have shot down two of Ukraine's army helicopters during an "anti-terror" operation in the eastern city of Sloviansk, Kiev has said.
It said a pilot and serviceman had been killed, four suspected separatists held and 10 rebel checkpoints seized.
Half of the city was later declared "under control" of the Ukrainian units.
There has been no independent confirmation of the claim. Separatists at three checkpoints earlier told the BBC they were still in control there.
Russia said the use of the army by Kiev against its own people was "leading Ukraine to catastrophe" and it has called for an emergency meeting of the United Nations Security Council in New York on Friday.
Describing the military operation as "punitive", the Russian foreign ministry also urged Western powers to give up their "destructive" policy on Ukraine.
Sloviansk is a stronghold for pro-Russian separatists who are exerting increasing control in the region.
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.
In other developments:
- Unknown attackers have seized a local railway control centre near Donetsk, disrupting train movement
- Pro-Russian rebels have left the city council office and TV centre in the eastern Luhansk region
- Several Western journalists were detained in Sloviansk, but all are now believed to be free
- In southern Ukraine, there are clashes between pro-Russian and pro-Kiev protesters in Odessa, with reports of gunfire and one person killed
'Full combat alert'
Ukraine's anti-terror centre said in a statement that "half of the city" of Sloviansk was under control of its units at 12:00 local time (10:00 GMT).
It said pro-Russian gunmen were using snipers and also mobile units dressed in riot police uniforms.
Meanwhile, the commander of Ukraine's National Guard said his units "practically cleared Sloviansk from terrorists".
Earlier, Interior Minister Arsen Avakov said the "active phase" of the operation in the Sloviansk-Kramatorsk region began at 04:30 local time.
"A real battle with professional mercenaries is going on," Mr Avakov said, adding that the separatists were using the tactics of hiding behind civilians in residential buildings.
Russia's state-run Rossiya 24 TV channel said the city was being "stormed".
It quoted Sloviansk's rebel commander Igor Strelkov as saying that the city was completely sealed off.
The fighting appeared to be concentrating on the periphery of the city, says the BBC's Sarah Rainsford, who is in the regional capital Donetsk.
In a video posted on YouTube, Sloviansk's self-declared mayor Vyacheslav Ponomaryov said "our city is under attack".
He appealed to children, women and the elderly not to leave their homes.
Local residents were later quoted as saying that the situation in the city had calmed down but remained tense.
Ukraine's acting president has said his forces are "helpless" in some parts of the east, and the country is now on full combat alert amid fears that Russian troops could invade.
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.