KIEV, Ukraine — Witnesses in the Ukrainian port city of Mariupol reported sustained explosions outside the city and a volunteer battalion of Ukrainian fighters says Grad rockets were fired at its positions late Saturday, little more than a day after Ukraine and Russian-backed separatist rebels signed a cease-fire following more than four months of fighting in the country’s east.

The cease-fire had appeared to largely been holding during much of the day.

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A burned Ukrainian army tank is seen near a destroyed kindergarten in the village of Kominternove, Ukraine, on Saturday. The Associated Press

But late Saturday, witnesses in Mariupol told The Associated Press by telephone that heavy explosions were coming from the city’s eastern outskirts, where Ukrainian troops retain defensive lines against the rebels.

The volunteer Azov Battalion said on Facebook that its positions were hit by Grad rockets, but did not give details.

Mariupol is a port city of about half a million on the coast of the Sea of Azov. Rebels recently opened a new front on the coast, leading to fears that the separatists were trying to secure a land corridor between Russia and the Crimean Peninsula, which Russia annexed in March.

Earlier Saturday, the presidents of Ukraine and Russia said the cease-fire was mostly holding, but the truce still appeared fragile as both sides of the conflict claimed violations.

A statement from Ukrainian President Petro Poroshenko’s office said he and Russian President Vladimir Putin discussed steps “for giving the cease-fire a stable character” in a telephone conversation Saturday.

But, it said, both leaders assessed the cease-fire as having been “fulfilled as a whole.” A separate Kremlin statement about the call said, “There was a mutual satisfaction with the fact that the sides of the conflict were overall observing the cease-fire regime.”

Col. Andriy Lysenko, a spokesman for Ukraine’s national security council, told reporters that rebels had fired at Ukrainian forces on 10 occasions Friday night after the cease-fire took effect.

In Donetsk, the largest city controlled by the Russian-backed separatists, the night passed quietly – a rarity after several months of daily shelling in residential areas. But Alexander Zakharchenko, the top separatist leader from Donetsk, told the Russian news agency RIA Novosti that the cease-fire had been violated with two rounds of shelling in the town of Amvrosiivka, about 30 miles southeast of Donetsk. He didn’t say when the supposed breach occurred.

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