Avakov said he could not specify the death toll but that he assumed that dozens of people had been killed.
He said that law-enforcement bodies were in control of the International Donetsk Airport.
"We reacted to the seizure of the airport: as a result, the airport is fully controlled (by the Ukrainian military)," Avakov said. "The enemy has suffered serious losses; we haven't had any casualties."
"The military operation in the southeast of the country is continuing," he added.