Blasts from the area near the airport were powerful enough to be heard in downtown Donetsk, the main rebel-held city in eastern Ukraine.
A spokesman for Ukraine's national security council, Volodymyr Polyovyi, said at a briefing in Kiev that rebels appeared to have tried to attack the airport, which has been under the control of government troops since May and has come under unremitting attacks from pro-Russia separatist rebels since then.
Shelling also occurred overnight on the outskirts of the port city of Mariupol, where Ukrainian troops retain defensive lines against the rebels.
The city council there said one civilian was killed and a serviceman was wounded. A shell also destroyed a nearby gas station and the volunteer Azov Battalion said on Facebook that their positions were hit by Grad rockets, but did not give details.
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Ukraine, Russia and the Kremlin-backed separatists signed the cease-fire deal in the Belarusian capita, Minsk, on Friday in an effort to end more than four months of bloodshed.
The negotiators also agreed on the withdrawal of all heavy weaponry, the release of all prisoners and the delivery of humanitarian aid to devastated cities in eastern Ukraine.
Ukrainian President Petro Poroshenko's office yesterday said he and Russian President Vladimir Putin had discussed steps "for giving the cease-fire a stable character" in a telephone conversation.
But, it said, both leaders assessed the cease-fire as having been "fulfilled as a whole.