Occasional shelling thundered around a flashpoint east Ukraine town on Sunday despite a new, shaky ceasefire that took hold along the rest of the frontline dividing Ukrainian forces and pro-Russian separatists.

The sporadic bombardments targeting the key railway hub of Debaltseve -- where thousands of Ukrainian soldiers are mostly surrounded by the rebels -- were audible some kilometres (miles) away. Their intensity was far less than before the truce came into effect at 2200 GMT Saturday.

Ukraine's military said that across the entire conflict zone, its soldiers' positions had come under fire from the rebels 60 times on Sunday. Debaltseve, it said, was "the main hotspot".

The pro-Russian insurgents "shot using every kind of weapon, including Grad (multiple) rockets," military spokesman Anatoliy Stelmakh told AFP.

"The rebels tried to storm our positions three times," he said, stressing that the Ukrainian forces were "only responding to attacks" and not instigating any themselves.

Stelmakh added, though, that "in general, the amount of Grad rocket fire has gone down across the whole conflict zone".

The separatists for their part said the truce was largely holding, but accused the other side of occasional breaches.

In Paris, French President Francois Hollande declared that observance of the ceasefire was "generally satisfactory" despite some "local incidents".

Hollande -- who, with German Chancellor Angela Merkel, had helped mediate the ceasefire agreed on Thursday -- was speaking after a four-way telephone conversation with Merkel and the leaders of Ukraine and Russia.

The truce is meant to be the first step of a peace plan aimed at ending 10 months of conflict that have claimed more than 5,480 lives.

The next phase is scheduled to see both sides pull their heavy weaponry back from the frontline within 48 hours of the ceasefire coming into effect, theoretically by 2200 GMT Monday.

Kiev is to start retaking control from the rebels over its 400-kilometre (250-mile) border with Russia, but only after local elections are held in the east by the end of the year. Under the deal, separatist-held territories are to be granted a degree of autonomy that will be established through talks.

But trust is low on all sides, and scepticism reigns after the collapse of a similar ceasefire agreed in September.

AFP journalists near Debaltseve said they heard sporadic artillery fire around the town on Sunday. They were unable to get closer because of the hostilities.

The strategic transport hub is seen as the position most likely to cause the latest ceasefire to fail. Ukrainian President Petro Poroshenko has warned that the truce was "threatened" by the separatist action there.

Rebels have warned that any attempt to move the thousands of government troops they claim to have trapped in Debaltseve will be seen as aggression and prompt a response.

Observers from the Organization for Security and Cooperation in Europe (OSCE) who are mandated to monitor the truce say rebels had blocked their access to the town.

The ceasefire was "overall respected" but there was at least one exchange of artillery around Debaltseve, according to the OSCE.

In the town of Yenakieve, some 20 kilometres (12 miles) from Debaltseve, a rebel commander named Alexei said he saw the truce as hollow.

"There is no ceasefire around Debaltseve and there won't be one. Shooting continues," he told AFP.

Ukraine's military said earlier Sunday that rebels were still trying to occupy the village of Chornuhine, some four kilometres from Debaltseve, and were moving heavy weaponry closer to the key government-held port city of Mariupol.

In Donetsk, a major rebel-held city in the east, residents welcomed the halt in fighting as the sound of constant bombardments died down. But they remained wary.

"I have trouble believing that the ceasefire will be respected for long," pensioner Andrei, 77, told AFP.

"But even if it lasts a few days, then that isn't bad."

International pressure is high on both sides to stick to the latest deal and prevent an escalation of the worst East-West crisis since the end of the Cold War.

Washington and Kiev accuse Moscow of fuelling last-gasp fighting that occurred just ahead of Saturday's ceasefire by pouring arms across the border to help rebels grab territory. Moscow denies the claims.

US Secretary of State John Kerry spoke by telephone with Russian Foreign Minister Sergei Lavrov on the weekend to underline "the importance of full implementation" of the ceasefire.

The EU has warned it could toughen its sanctions on Russia if the situation fell apart, while US President Barack Obama has warned he could start supplying arms to Ukraine if the truce collapses.

Russian President Vladimir Putin was said to have reaffirmed his commitment to the peace deal in a call with Merkel and Hollande.

The UN Security Council is expected to meet in emergency session Sunday to shore up the truce.