Ukrainian troops have set up positions around the airport in Kramatorsk
Russian President Vladimir Putin has warned that Ukraine is "on the verge of civil war" after Kiev sent in troops against pro-Russia separatists.
Mr Putin, in a phone call to German Chancellor Angela Merkel, described the move as a "sharp escalation".
Ukraine announced the start of an "anti-terrorist operation" in the east of the country on Tuesday.
Moscow annexed Crimea last month and is believed to have thousands of troops massed along its border with Ukraine.
"The Russian president remarked that the sharp escalation of the conflict has placed the country, in effect, on the verge of civil war," the Kremlin said of Mr Putin's conversation with Mrs Merkel.
But it said that both leaders "emphasised the importance" of planned four-way talks on Thursday between senior diplomats from Russia, the EU, the US and Ukraine.
Buildings seized
The Kremlin statement described the Ukrainian military operation in eastern Ukraine as an "anti-constitutional course to use force against peaceful protest actions".
Tensions have mounted in recent days after pro-Russian rebels seized buildings in about 10 towns and cities across eastern Ukraine.
They are demanding greater autonomy or referendums on secession from Ukraine.
Ukrainian acting President Olexander Turchynov said on Tuesday that troops had regained control of a military airfield in Kramatorsk after fighting with armed pro-Russian groups.
Barricades have been strengthened outside the occupied mayor's office in Sloviansk
Pro-Ukrainian rallies have also been held in eastern towns, like here in Luhansk
He said the aim of the operation in the east was to "protect Ukrainian citizens, to stop the terror, to stop the crime, to stop the attempts to tear our country apart".
Overnight, up to 100 people were reported to be outside the airbase with petrol bombs lined up on the ground.
Ukrainian armoured vehicles have been assembling north of the nearby town of Sloviansk.
"They [separatists] must be warned that if they do not lay down their arms, they will be destroyed," Ukrainian Security Service General Vasyl Krutov told reporters.
Russia's foreign ministry has expressed "deep concern" at reports of casualties in eastern Ukraine, but these could not be confirmed.
Kiev and Washington have accused Russia of fomenting the unrest, something Moscow strongly denies.
The White House has described Ukraine's military operation as a "measured" response to a lawless insurgency.
Russia took control of the Ukrainian region of Crimea last month, after it held a controversial referendum on self-determination.
The US has said it is "seriously considering" adding to sanctions imposed after the annexation of Crimea.
