Officials in Ukraine say armed forces have shot dead up to five militants in the town of Slavyansk, which has been under the control of pro-Russian gangs for days.
They also claim to have destroyed three checkpoints the groups had set up.
Meanwhile Moscow has accused the West of playing a 'geopolitical game' in Ukraine, saying it helped bring about the downfall of the country's former president Viktor Yanukovych.
Foreign Minister Sergei Lavrov claimed the US and EU were behind the uprising that ousted Viktor Yanukovych, the pro-Kremlin president of Ukraine, in February.
"In Ukraine, the United States and the European Union tried to stage - let's call things what they are - another 'colour revolution', an operation to unconstitutionally change regime," the Interfax news agency quoted Mr. Lavrov as saying.
Obama: Russia not doing enough
"Our Western partners, first and foremost the United States, tried to behave as winners in the Cold War and pretend that one can ignore Russia in European affairs and undertake activities that directly damage Russian security interests".
Mr. Lavrov added that Ukraine was being used as a "pawn in geopolitical game" against Russia. He also said the West had tried to "besmirch the Olympic Games in Sochi through every means possible" as part of "anti-Russian propaganda".
Meanwhile, Russia's Gazprom has sent an US$11.4 billion (€8.24bn) gas bill to Ukraine energy firm Naftogaz - five times the original amount.
It comes as US President Barack Obama warns Moscow could face "consequences" after accusing the Kremlin of not honouring an international agreement aimed at defusing the Ukraine crisis.
Mr. Obama says Vladimir Putin has so far failed to abide by the "spirit or the letter" of the Geneva deal - with pro-Russian militias still in control of towns and buildings in eastern Ukraine.
He says there is no "military solution" to the conflict, but conceded that Russia is unlikely to change course and end the stand-off.
President Obama says Moscow could now face further sanctions.
Speaking on his current tour of Asia, the US President claimed Russia was not doing anything to deter the militants.
