The US has urged Russia to "leave Ukraine in peace" and warned that "every inch" of territory in neighbouring Nato states would be defended if threatened.
US Secretary of State John Kerry said that Russia had failed to abide by the terms of a de-escalation agreement.
Russia's President Putin insisted that his country had no troops in Ukraine.
The comments came after pro-Russia activists stormed several more buildings in eastern Ukraine.
Mr Kerry said that Russia had "escalated the crisis" since signing the de-escalation agreement last month.
"Not one single step has been taken by Russia in any public way that seriously attempts to live by the spirit or the law of what was signed in that agreement" he said.
He went on to say that Nato was facing a "defining moment" in the strength of its alliance in the face of Russian actions.
Moscow has said it has no intention of invading eastern Ukraine, where pro-Russia activists have seized government buildings in more than a dozen towns and cities.
"I solemnly declare that there are no Russian instructors there, nor any special forces there, nor troops," said Mr Putin.
Mr Putin also warned that new EU and US sanctions against Russia could impact on the work of Western energy firms.
"If this continues, we will of course have to think about how (foreign companies) work in the Russian Federation, including in key sectors of the Russian economy such as energy," he said.
In Kiev on Tuesday, activists mourning those who died in protests against the then pro-Moscow government earlier this year took part in a torch-lit ceremony.
They clashed with members of a far-right movement who also tried to join the march.