Arsen Avakov said it began when unidentified gunmen tried to storm local administration buildings and police fired back.
Several other official buildings were reported to have been seized in eastern Ukraine on Saturday.
The confrontations come amid rising tension between the new government and pro-Russia protesters.
Earlier, gunmen occupied a police station and a security services building in the town of Sloviansk. Official buildings in Druzhkovka were also reported to have been taken over.
A Donetsk regional police chief also quit after pro-Russia crowds marched on a police station demanding his resignation.
Eastern Ukraine has a large Russian-speaking population and has seen a series of protests since the ousting of pro-Russian President Viktor Yanukovych in February.
The new government in Kiev accuses Moscow of orchestrating the unrest in eastern Ukraine. But Russia denies responsibility.
Protesters in largely Russian-speaking Donetsk, 80 miles from Sloviansk, have been occupying government buildings for days and demanding a referendum on becoming part of Russia.
Trouble continued in several towns and cities on Saturday despite the Kiev government setting a deadline of Friday for all occupations to end.
“Kramatorsk. An attack is under way. Unknown persons fired shots at the district police department. The police are firing shots in response. A shootout is under way,” Arsen Avakov wrote on his Facebook page late on Saturday.
He also reported that an attack on police buildings in Krasny Liman late in the day had been repelled. The gunmen there had been equipped with Russian-made Kalashnikov assault rifles, he added.
There were no reports of casualties in Kramatorsk or Krasny Liman and Arsen Avakov’s comments could not be independently verified.
Earlier, in the town of Sloviansk, dozens of unidentified armed men in camouflage uniform seized the police station and security service premises.
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