Gunfire could be heard from the airfield at the town of Kramatorsk after a fighter jet swooped low over the area.
Ukrainian troops were seen disembarking from helicopters.
A Reuters correspondent in Kramatorsk saw four military helicopters over the airport.
Two of these landed and when troops stepped out and walked across the field, locals manning a barricade shouted "Shame! Go back home!" Ukraine's acting President Oleksander Turchinov had earlier announced that a military operation was under way to flush pro-Russian separatists out of the government buildings and facilities they have seized in about 10 towns and cities in the east over the last few days.
Turchinov issued a statement saying Ukraine had retaken the airfield in Kramatorsk from pro-Russian militants, while the state security service said an "anti-terrorist" operation was in progress against separatists in the nearby town of Slaviansk.
The operations appeared to mark an escalation of the deepest East-West crisis since the Cold War.
The standoff has raised fears in the West and in Kiev that Russia might intervene militarily on behalf of Russian speakers in eastern Ukraine.
That follows its annexation of the Crimean region last month in response to the overthrow of Ukraine's pro-Moscow president, Viktor Yanukovich, after weeks of protests.
Earlier, pro-Russian militants who had been holed up in the Kramatorsk police headquarters since Saturday left the building -but a state security official in Kiev said separatists had then taken over the agency's offices in the town.
The reports of military action in eastern Ukraine caused Russian shares to fall sharply, with the main Moscow indices down about 3%.
Russian Prime Minister Dmitry Medvedev gave a gloomy assessment, apparently referring to the deaths of at least two people on Sunday when Kiev unsuccessfully tried to regain control in Slaviansk, about 150km (90 miles) from the Russian border.
"Blood has once again been spilt in Ukraine. The country is on the brink of civil war," he said on his Facebook page.
Turchinov said an offensive he first announced on Sunday was now in progress after days in which it failed to materialise. "The anti-terrorist operation began during the night in the north of Donetsk region. But it will take place in stages, responsibly, in a considered way.
"I once again stress: the aim of these operations is to defend the citizens of Ukraine," he told parliament.
At least 15 armoured personnel carriers displaying Ukrainian flags were parked by the side of a road around 50km (30 miles) north of Slaviansk, witnesses said.
Ukrainian troops wearing camouflage gear and armed with automatic weapons and grenade launchers were stationed nearby, with a helicopter and several buses containing interior ministry personnel near the road.
In Slaviansk itself, separatists have seized the local headquarters of the police and state security service.