REUTERS/Vasily Fedosenko A local man rides a motorcycle past a truck burned by recent shelling on the outskirts of the southern coastal town of Mariupol September 7, 2014.
The accord, brokered by envoys from Ukraine, the separatist leadership, Russia and Europe's OSCE security watchdog, is part of a peace plan intended to end a five-month conflict that has killed nearly 3,000 people and caused the sharpest confrontation between Russia and the West since the Cold War a generation ago.
Shelling resumed near the port of Mariupol on the Sea of Azov late on Saturday night, just hours after Russian President Vladimir Putin and Ukrainian counterpart Petro Poroshenko had agreed in a phone call that the truce was holding.
Fighting also broke out early on Sunday on the northern outskirts of rebel-held Donetsk, the region's industrial hub. A Reuters reporter saw plumes of black smoke filling the sky near the airport, which has been in the hands of government forces.
"Listen to the sound of the ceasefire," joked one armed rebel. "There's a proper battle going on there."
Early on Sunday afternoon both cities were calm again.
Reuters
Map locating recent clashes between pro-Russian separatists and Ukrainian forces.
Both sides insisted they were strictly observing the ceasefire and blamed their opponents for any violations.
"As far as I know, the Ukrainian side is not observing the ceasefire. We have wounded on our side at various points. We are observing the ceasefire," Vladimir Antyufeyev, deputy premier of the self-proclaimed "Donetsk People's Republic", told Reuters.
Earlier, government forces said they had come under artillery fire east of Mariupol, a crucial port for Ukrainian steel exports. In the days before the ceasefire they had been trying to repel a big rebel offensive against the city.
The shelling in Mariupol claimed the first civilian casualty since the ceasefire began. Local officials confirmed the death of a 33-year-old woman early on Sunday and said at least four other people had been wounded.
"They, terrorists, Russians, are trying to scare us. They have no respect for the ceasefire. They are lying all the time. They are people with no honour," said Slavik, a Ukrainian soldier armed with a machine gun.
REUTERS/Maxim Shemetov
A pro-Russian separatist checks an automatic grenade launcher mounted in a vehicle at a check point on the outskirts of Donetsk September 6, 2014.
"MONSTERS"
"We left this area the day before yesterday. Everyone saw us pulling out tanks in line with the agreement. We only left lightly armed people to man checkpoints and these monsters violated every word of the agreement," he said.
A Reuters reporter at the scene, a few km (miles) from the centre of the city of 500,000, saw fires raging just before midnight on Saturday as Ukrainian reinforcements raced east towards the demarcation line separating the two sides.
Poroshenko agreed to the ceasefire after Ukraine accused Russia of sending troops and arms onto its territory to bolster the separatists after they suffered heavy losses over the summer to a Ukrainian government offensive.
Moscow denies dispatching forces or arming the rebels despite what NATO says is overwhelming evidence to the contrary.
The peace roadmap agreed on Friday includes an exchange of prisoners of war and the establishment of a humanitarian corridor for refugees and aid.
Russia's Interfax news agency reported that the first PoWs were handed over to Ukrainian government forces late on Saturday but this report could not be confirmed immediately.
Poroshenko spent Thursday and Friday at a NATO summit in Wales at which U.S. President Barack Obama and other leaders urged Putin to pull forces out of Ukraine. NATO also approved wide-ranging plans to boost its defences in eastern Europe in response to the Ukraine crisis.
REUTERS/Gleb Garanich
A Ukrainian serviceman passes by an armoured vehicle at checkpoint in Karlovka near Donetsk September 6, 2014.
The Ukraine conflict has revived talk of a new Cold War as the West accuses Putin of deliberately destabilising the former Soviet republic of 46 million people. Ukraine's prime minister accused Putin of striving to re-create theSoviet Union.
Putin says he is defending the interests of ethnic Russians facing discrimination and oppression in Ukraine since protesters topped Kiev's pro-Russian president in February. He has seen his popularity in Russia soar since Russia annexed Ukraine's Black Sea peninsula of Crimea, which has a Russian majority, in March.
The European Union announced new economic sanctions against Russia late on Friday over its role in Ukraine but said they could be suspended if Moscow pulled out its troops and honoured the ceasefire conditions.
Russia's foreign ministry responded angrily, pledging unspecified "reaction" if the new sanctions were implemented. Moscow responded to a previous round of U.S. and EU sanctions by banning most Western food imports.
(Writing by Gareth Jones; Editing by Mark Heinrich)