Russia's Foreign Minister Sergei Lavrov has said armed action by Ukrainian authorities in the east of Ukraine could undermine forthcoming talks.
Kiev earlier warned pro-Russian militants who stormed police stations in eastern towns on Saturday that they would be harshly dealt with.
The US has accused Russia of "inciting" trouble in eastern Ukraine.
Four-party talks involving Ukraine, Russia, the US and the EU are due to start in Geneva on Thursday.
Mr Lavrov said Ukraine was "demonstrating its inability to take responsibility for the fate of the country".
Early on Sunday, Ukrainian Interior Minister Arsen Avakov announced that an "anti-terror" operation had begun in Sloviansk, one of the towns where armed men had stormed a police station.
Russia has so far denied that it is directly responsible for the unrest.
But the US says there has been a "concerted campaign" by forces with Russian support to undermine the authorities in Kiev.
In a phone call, US Secretary of State John Kerry urged his Russian counterpart to de-escalate the situation or face additional consequences.
He said the raids were similar to those which preceded the Russian annexation of Crimea earlier this year.
"If Russia does not take steps to de-escalate in eastern Ukraine and move its troops back from Ukraine's border, there will be additional consequences" he warned.
It has also been announced that US Vice President Joe Biden is to travel to Ukraine in 10 days' time.
On Saturday, armed men took over police stations and official buildings in three eastern towns.
Heavy gunfire was heard as dozens of men stormed police headquarters in Kramatorsk.
They were reported to have arrived in buses and to have used automatic weapons to overwhelm police.
Militants took over official buildings in the towns of Sloviansk and Druzhkovka.
They also continued their occupation of the main administrative building in the regional capital Donetsk, which they have held for one week.
Eastern Ukraine has a large Russian-speaking population and has seen a series of protests since the ousting of Ukraine's pro-Russian President Viktor Yanukovych in February.
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