"Armed people in camouflage uniform have seized a district police station in Slavyansk. Response will be very tough here," Avakov said.
A special police group was sent to Slavyansk, he said.
The Ukrainian Interior Ministry would respond toughly to attempts to destabilize the situation, especially in the southeast of the country, the ministry said in a statement on its website on Saturday.
"The Interior Ministry will toughly respond to attempts to intentionally destabilize the situation, violation of public order and mass disorders all over Ukraine's territory, particularly in regions, where special operations are conducted to settle the situation -- the Donetsk, Lugansk and Kharkov regions. All who will violate the law, irrespective of declared slogans and party affiliation, will be detained," the statement reads.
The ministry warned that a "serious" article of the Ukrainian Criminal Code would be applied to organizers of protests.
Meanwhile, according to reports from Donetsk, dozens of people got into the Donetsk regional prosecutor's office overnight.
Unknown people took a guard and a cleaning woman out of the building, but shortly after that, law enforcers arrived on the scene and removed all from the building, local media reported. There were no comments from the prosecutor's office and the Donetsk city police department, where telephone calls were not answered.
A group of unidentified people seized a district police station in Slavyansk, the Donetsk region, on Saturday, an official at the Donetsk regional police department told Itar-Tass on Saturday.
"Unknown people have seized a district police station today. They were in camouflage uniform. They remain there now," he said.