Donetsk is one of the remaining rebel strongholds in restive eastern Ukraine, and the focus of a government-led counter-terrorism operation.
"The active stage of the counter-terrorist operation continues," Ukrainian military spokesman Vladislav Seleznev told CNN. "The government is now at full control of the airport and the road leading to it."
A warning from the Donetsk City Council directed residents to stay inside.
According to the statement, the city council reported gunfire and explosions near the airport and the Zhovtneva Mine compound. Power outages continued, and the Zakdidny bus terminal was closed.