Ukrainian armed forces have begun a "special operation" against militiamen in the country's Russian-speaking east.

Authorities in the capital Kiev said the armed forces had recaptured a military airfield from pro-Russia separatists.

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 reported 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 Turchynov had earlier announced that a military operation was under way.

They are trying to flush out pro-Russian separatists from the government buildings and facilities they had seized in about ten towns and cities in the east over the last few days.

Mr Turchynov issued a statement saying Ukraine had retaken the airfield in Kramatorsk from pro-Russian militants.

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 stand-off has raised fear in the West and in Kiev that Russia might intervene militarily on behalf of Russian speakers in eastern Ukraine.

A spokesman for US President Barack Obama said Ukraine's government was obliged to respond to "provocations" in the east.

The White House said it was not considering sending arms to Kiev, but said it was "seriously considering" adding to sanctions imposed after the annexation of Crimea.

However, the State Department said such action was unlikely before a meeting in Geneva on Thursday at which the US, EU and Ukrainian officials will try to persuade Russia to defuse the situation.

The latest tense episode follows Russia's annexation of the Crimean region last month in response to the overthrow of Ukraine's pro-Russia president, Viktor Yanukovych, after weeks of protests.

Earlier, pro-Russian militants who had been holed up in the Kramatorsk police headquarters since Saturday left the building.

However, a state security official in Kiev said separatists had then taken over the agency's offices in the town.

Russian Prime Minister Dmitry Medvedev gave a gloomy assessment, apparently referring to the deaths of at least two people on Sunday when Ukraine unsuccessfully tried to regain control in Slaviansk, about 150km 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.

Mr Turchynov 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 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.

Russia has accused Ukraine of provoking the crisis by ignoring the rights of citizens who use Russian as their first language, and has promised to protect them from attack.

Russia also stressed the presence of far-right nationalists among Ukraine's new rulers.

However, a UN report cast doubt on whether Russian-speakers were seriously threatened, including those in Crimea who voted to join Russia after Russian forces had already seized control of the Black Sea peninsula.

"Although there were some attacks against the ethnic Russian community, these were neither systematic nor widespread," said the report by the UN human rights office.

Russia called the report one-sided, politicised and apparently fabricated.

The United Nations has said Secretary-General Ban Ki-moon has spoken with Russian President Vladimir Putin.

It said Mr Ban voiced alarm about the escalating crisis in Ukraine and that a worsening situation would be detrimental for all.

NATO Secretary-General Anders Fogh Rasmussen accused Russia of involvement in the rebellions.

"It is very clear that Russia's hand is deeply engaged in this," he told reporters.

Russian Foreign Minister Sergei Lavrov denied that Russia was stirring up the separatists in the east and southeast as a possible prelude to repeating its annexation of Crimea.

"Ukraine is spreading lies that Russia is behind the actions in the southeast," Mr Lavrov said on a visit to China.

Russia has demanded constitutional change in Ukraine to give more powers to Russian-speaking areas, where most of the country's heavy industry lies, while the rebels have demanded Crimean-style referendums on secession in their regions.