One civilian has been killed in shelling in the Ukrainian port city of Mariupol and large explosions have been heard near the airport in Donetsk, raising fears that a ceasefire signed two days ago is on the verge of collapse.

Blasts from the area near the airport were powerful enough to be heard in downtown Donetsk, the main rebel-held city in eastern Ukraine.

Al Jazeera's Paul Brennan, reporting from Donetsk, said an exchange of grad rockets and the use heavy machine guns could be heard in the vicinity of the airport.

"The thought that the ceasefire would lead to an end to the violence has not proven to be accurate around the airport," he said.

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 separatists since then.

The ceasefire had appeared to be holding for much of the day on Saturday, but shelling started late at night.

A rebel statement said Ukrainian forces violated the ceasefire by firing on their positions in six locations on Saturday, including near the Donetsk airport.

The statement said several rebels were killed.

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.

John Wendle, reporting for Al Jazeera from near Mariupol, said heavy calibre machine guns had also been heard near the city

He said pictures he had seen showed civilian cars destroyed in the attack.

Reuters also reported that lorries carrying pro-government militia volunteers and tanks and armoured personnel carriers were seen heading towards the site of the attack.

The city of 500,000 people on the Sea of Azov near the Russian border had been the scene of fierce fighting between Ukrainian government forces and pro-Russian separatists before the ceasefire deal.

Earlier Saturday, the presidents of Ukraine and Russia said the ceasefire was mostly holding.

A statement from the Ukrainian president, Petro Poroshenko, said he and Russian counterpart Vladimir Putin discussed steps "for giving the ceasefire a stable character'' in a telephone conversation Saturday.

Europe's OSCE security watchdog approved the ceasefire in Minsk on Friday as part of a peace agreement that also includes an exchange of prisoners of war and establishing a humanitarian corridor for refugees and aid.