The presidents of Ukraine and Russia on Saturday said the cease-fire between Ukrainian forces and Russian-backed rebels was mostly holding, but the truce still appeared fragile in its first full day 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 was to take 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 50 kilometers (30 miles) southeast of Donetsk.

"At this time the cease-fire agreement is not being fully observed," he said. He didn't say when the supposed breach was to have occurred.

Lysenko said Ukrainian forces were strictly observing the cease-fire and suggested that Zakharchenko's claim was a provocation.

Earlier Saturday, the mayor's office in Donetsk said there had been no reports of shooting or shelling there although some shelling had been heard late Friday afternoon. The city council of the second-largest rebel-held city of Luhansk, which had endured intense fighting for weeks, also reported the night was quiet.

Along the coast of the Sea of Azov, where rebels allegedly backed by Russian troops opened a new front two weeks ago, government and separatist forces were keeping a distance of about 20 kilometers (12 miles) between them, according to an AP reporter. The remains of a Ukrainian tank smashed by rocket fire lay along the road, evidence of the fighting that raged until just before the cease-fire.

Ukraine, Russia and the Kremlin-backed separatists signed the cease-fire deal Friday in Minsk, the Belarusian capital, in an effort to end more than four months of fighting in the region. 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.

If the ceasefire holds, it would be a landmark achievement for both sides. Fighting between pro-Russian rebels and Ukrainian government troops has ravaged the already teetering Ukrainian economy, claimed at least 2,600 civilian lives and left hundreds of thousands homeless, according to United Nations estimates.

The country also faces escalated tensions between the Russian-speakers who predominate in the rebel east and the Ukrainian-speakers in the central and western reaches.

In a sign of the simmering anger, the head of one of Ukraine's two main Orthodox churches on Friday issued a fierce rebuke of Putin, claiming the he, like the Biblical Cain, was under the influence of Satan.

"For the sake of his pride, he continues to multiply evil," wrote Patriarch Filaret, head of the Ukrainian Orthodox Church-Kiev Patriarchate.

That church competes for influence in Ukraine with another Orthodox faction that is under the Moscow Patriarchate.

Western leaders voiced skepticism over Russia's commitment to the deal. A previous 10-day cease-fire, which each side repeatedly accused the other of violating, yielded few results at the negotiating table.

U.S. President Barack Obama said he was hopeful the cease-fire would hold but unsure the rebels would follow through.

"It has to be tested," Obama said Friday at the closing of a two-day NATO summit in Wales.

Both the U.S. and the European Union have prepared even tougher sanctions on Moscow, and Obama stressed that the most effective way to ensure the cease-fire's success was to move ahead with those measures and maintain pressure on Russia. According to an EU diplomat, these new measures would target Russia's access to capital markets and trade in arms and defense technology, dual-use goods and sensitive technologies. The new sanctions were given preliminary approval Friday night and could be implemented as early as Tuesday.

"If certain processes get underway, we are prepared to suspend sanctions" against Russia, German Chancellor Angela Merkel said.

In a statement published online Saturday, Russia's foreign ministry condemned further EU sanctions and promised that "there will undoubtedly be a reaction from our side" to any new measures. In August, Russia passed a sweeping ban on meat, fruit, vegetables, and dairy product imports from the EU, the U.S. and a host of other countries who imposed sanctions on Russia.

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Mills reported from Moscow. Peter Leonard in Mariupol, Ukraine, contributed to this report.