Donetsk, Ukraine--Fighting dropped sharply across eastern Ukraine on Sunday but there was still sporadic shooting after a ceasefire came into force, the first step in a fragile peace plan aimed at ending 10 months of conflict.
An elderly man and woman died after a Grad missile fire hit the town of Popasna in the Lugansk region some 20 minutes after the truce began at midnight (2200 GMT Saturday), pro-Kiev local governor Gennadiy Moskal said.
The firing allegedly came from an area which Kiev says is under the command of a renegade group of Cossack fighters who insist they will not obey rebel leaders' commands to lay down their guns.
Elsewhere across conflict zone, Ukraine's military said its forces had come under fire 10 times but that shooting had tailed off since 3:00 am (0100 GMT).
"In general the situation in east Ukraine appears to be heading towards stabilisation," military spokesman Andriy Lysenko said.
The rebels' defence ministry also said the truce was being "generally respected".
The latest deal between Ukraine and the rebels, hammered out Thursday after marathon talks involving the leaders of Ukraine, Russia, Germany and France, is seen as the best hope to stop fighting that has killed over 5,480 people since April.
But trust is low on all sides and scepticism remains high after the collapse of previous ceasefires, also signed in the Belarussian capital Minsk.
AFP reporters heard several mortars fired near the frontline in rebel bastion Donetsk around midday Sunday and the sound of occasional firing from the direction of the battered town of Debaltseve.
The situation remains most fraught around the vital transport hub, where pro-Russian rebels waged fierce battles to surround Ukranian forces in the hours leading up to the truce.
Deputy regional police chief Ilya Kiva told AFP that shooting in Debaltseve and the nearby village of Chornuhine had dropped off but not stopped entirely.
"We hope that it will just take a bit of time before we get a full ceasefire. It is not an immediate process."
Ukraine's military said rebels were still trying to occupy Chornuhine, some four kilometres from Debaltseve, and were also moving heavy weaponry towards a village close to the key government-held port city of Mariupol.
Ukrainian President Petro Poroshenko warned as the truce started that the peace process was already "threatened" by the separatists' tightening the noose around Debaltseve.
Poroshenko has said he will introduce martial law across Ukraine if the ceasefire breaks down.
Rebels have warned that any attempt to move the thousands of troops they claim to have trapped in Debaltseve along the one -- almost impassable -- road that Kiev still tenuously holds will be seen as aggression and draw a response.
Securing Debaltseve, a railway hub linking Donetsk and Lugansk, is seen as vital for the separatists if they want to make their enclaves sustainable.
- International pressure -
Poroshenko is to speak later Sunday with Russian President Vladimir Putin and the two leaders who helped broker the ceasefire, German Chancellor Angela Merkel and French President Francois Hollande.
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.
US Secretary of State John Kerry spoke by telephone with Russian Foreign Minister Sergei Lavrov to underline "the importance of full implementation" of the ceasefire.
Washington and Kiev accused Moscow of fuelling the last-gasp fighting Saturday by pouring arms across the border to help rebels grab territory. Moscow denied the claims.
AFP