Arsen Avakov wrote on his Facebook page that “all security units” were involved in an “anti-terror operation” in the eastern city of Sloviansk.
Russia warned earlier that any use of force in eastern Ukraine could scupper crisis talks due later this week.
The US accuses Moscow of inciting the trouble. The Kremlin denies the charge.
Russia’s Foreign Minister Sergei Lavrov said the Kiev government was “demonstrating its inability to take responsibility for the fate of the country”.
The US said there had been a “concerted campaign” by forces with Russian support to undermine the authorities in Kiev.
US Secretary of State John Kerry warned of “additional consequences” if Russia failed to make efforts to “de-escalate” and pull its troops back from Ukraine’s border.
Four-party talks involving Ukraine, Russia, the US and the EU are due to start in Geneva on Thursday.
On Saturday, armed men took over police stations and official buildings in Sloviansk and two other eastern towns – Kramatorsk and Druzhkovka.
Similar reports emerged from Sloviansk and Kramatorsk of armed men dressed in camouflage arriving in buses and storming the police stations.
Pro-Russian demonstrators also continued their occupation of the main administrative building in the regional capital Donetsk, which they have held for one week.
Arsen Avakov labelled the actions a “display of aggression by Russia”.
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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