Ukraine's acting President Olexander Turchynov has announced the start of an "anti-terrorist operation" against pro-Russian separatists.
He told parliament it was being conducted "stage by stage, in a responsible... manner".
Hours later, gunfire was heard at an airbase which officials said had been in the hands of militants.
Russian President Vladimir Putin said the escalation of the conflict had put Ukraine "on the verge of civil war".
The Kremlin said Mr Putin made the warning in a phone call with German Chancellor Angela Merkel.
It said that both leaders "emphasised the importance" of planned talks in Geneva on Thursday between Russia, Ukraine, the US and the EU.
Mr Turchynov said the airbase at Kramatorsk had been "liberated" from "terrorists".
Pro-Russian rebels have seized buildings in about 10 towns and cities across Ukraine's eastern provinces, its industrial heartland.
Thousands of Russian troops are reported to be deployed along the border, kindling fears that any crackdown on the rebels could trigger an invasion.
Russia annexed the Ukrainian region of Crimea last month, after it broke away and held a controversial referendum on self-determination.
The White House on Tuesday described the Ukrainian government's response as measured, and warned it was "seriously considering" further sanctions against Russia.
President Putin, speaking earlier on Tuesday, said he expected the actions of Ukraine's government to be condemned by the international community.
The BBC's Gabriel Gatehouse in Kramatorsk reported that an angry crowd gathered outside the airbase, prompted by the arrival of two helicopters carrying soldiers they said had come from Kiev.
A crowd of some 200 people remained on Tuesday evening, chanting slogans in favour of a referendum on the region's future, our correspondent adds.
A spokesman for the Russian foreign ministry expressed "deep concern" at reports of casualties in eastern Ukraine, but these could not be confirmed.
Display of force
After days when there was little sign of the Ukrainian government exerting its authority in eastern Ukraine, Tuesday saw a very public display of force at a checkpoint just north of the Donetsk region, in the Kharkiv region, the BBC's Daniel Sandford reports.
But if Ukrainian forces attempt to move on to the town of Sloviansk, they will find what looked like very experienced soldiers on the pro-Russian side, our correspondent adds.
In other developments:
- Russian Finance Minister Anton Siluanov said the country's economy faced "the most difficult conditions since the 2008 crisis", with capital flight in the first quarter of this year of $63bn (£38bn; 46bn euros), because of "risks seen by the population and by investors"
- German utility company RWE AG said in a statement it had started supplying gas to Ukraine, which faces Russian cuts over unpaid bills
'Stop the terror'
Mr Turchynov 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".
Protesters gathered outside parliament in Kiev to demand action against the separatists.
There were reports overnight of gun attacks on rebel checkpoints near the Donetsk town of Sloviansk, where pro-Russian militants seized a police station and a security services building at the weekend.
A police building in Kramatorsk was also seized but the militants there have reportedly now handed back control to the police.
'Tanks or talks'
Russian Foreign Minister Sergei Lavrov warned that any use of force by the Ukrainian government in the east could undermine talks on the crisis involving the EU, Russia, the US and Ukraine, which are due to be held in Geneva on Thursday.
"You can't send tanks against your own citizens and at the same time hold talks," he said on a visit to China.
White House spokesman Jay Carney said later on Tuesday that the US was considering additional sanctions against Russia but would not be providing lethal aid to Ukraine.
In a statement, the Kremlin blamed the unrest in Ukraine's south-east on the "unwillingness and inability of the leadership in Kiev to take into account the interests of Russia and the Russian-speaking population".
Are you in eastern Ukraine? Have you been affected by the unrest? You can email your experiences to firstname.lastname@example.org using the subject line "Ukraine".