Pro-Russian protesters in Kharkiv threw tyres and plastic barriers on a fire at a government building
The Ukraine authorities say they have seized back control of the regional administration building in the eastern city of Kharkiv from pro-Russia separatists.
They say they hope buildings in Luhansk and Donetsk will be freed shortly as well.
On Monday, pro-Russia demonstrators seized government buildings in the three cities.
Russia recently annexed the peninsula of Crimea following a referendum.
Kiev and the West say the referendum in the territory, where the majority of people are Russian speakers, was illegal.
Moscow has thousands of troops massed along its border with eastern Ukraine.
Although it insists it has no intention of invading Ukraine, it says it reserves the right to defend ethnic Russians in the country.
Ukraine Deputy Foreign Minister Danylo Lubkivsky has told the BBC Radio 4's Today programme that the situation in eastern Ukraine was "under control but remains dangerous".
Interim President Oleksandr Turchynov says several Ukrainian policemen have been injured in the operation to free the Kharkiv regional state administration.
Some 70 people were held without shots being fired, Ukraine's interior ministry said in a statement.
Turchynov said those who seized the buildings would be treated as "terrorists and criminals" who would be prosecuted with the full force of the law.
Rebels occupying Donetsk's regional government building on Monday declared a "people's republic" and called for a referendum on secession from Ukraine to be held by 11 May.
There have been talks overnight in Donetsk between the authorities and pro-Russian activists who had occupied the regional administration building.
On Tuesday, Russia warned Ukraine to stop any military preparations, with the Russian foreign ministry saying in a statement that such preparations risked causing a civil war.
Russia is refusing to recognise the new authorities in Kiev who took power after pro-Moscow President Viktor Yanukovych was ousted in February.
'Whipping up tension'
On Monday, a White House spokesman warned Russia against "either overtly or covertly moving into eastern Ukraine".
He said there was "strong evidence" that some of the pro-Russia demonstrators there were being paid and were not local - and called on Russian President Vladimir Putin to "cease efforts" to destabilise the situation.
Moscow denies orchestrating instability and separatist sentiment in Ukraine's industrial heartland.
In an article on the website of the UK's Guardian newspaper, Russian Foreign Minister Sergei Lavrov condemned what he described as the "groundless whipping up of tension" - he said the West was to blame for what was happening , because it had tried to force Ukraine to make a choice between east or west.
He also warned authorities in Kiev against any use of force against pro-Russian demonstrators.
On Tuesday, the Russian foreign ministry alleged that Ukraine was deploying "US mercenaries" from a private security firm dressed as Ukrainian special forces - but there has been no confirmation of that, says the BBC's Steven Rosenberg in Donetsk.
This is part of the continuing war of words between Russia and the West, our correspondent says.
But amid the war or words, there is still some talk of diplomacy, our correspondent adds: senior diplomats from the United States, Russia, Ukraine and the European Union are expected to meet within the next 10 days in an effort to defuse the tension.
The US and the EU have already imposed targeted sanctions on Russian and Ukrainian individuals over the annexation of Crimea.
BBC Moscow correspondent Daniel Sandford says that although events in Donetsk appear similar to those in Crimea, there are major differences.
Donetsk has many Ukrainian speakers as well as a Russian-speaking majority, and opinion polls there have shown considerable support for a united Ukraine, he says.
Eastern Ukraine was the political heartland of Yanukovych and has a large Russian-speaking population.
Yanukovych fled Kiev for Russia after months of street protests triggered by his refusal to sign an association agreement with the EU in favour of closer ties with Russia. More than 100 people died in the ensuing unrest.