An elderly man and woman died after Grad missile fire hit the town of Popasna in the Lugansk region some 20 minutes after a truce came into force at midnight local time (2200 GMT yesterday), 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 stop firing.
Elsewhere across the region, Ukraine's military said its forces had come under fire 10 times but that shooting had tailed off since 3:00 am (0100 GMT).
The situation remained most fraught around the key government-held town of Debaltseve, where pro-Russian rebels battled fiercely to surround Ukranian forces in the hours leading up to the truce.
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Deputy regional police chief Ilya Kiva told AFP that firing 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 Kiev-held port city of Mariupol.
The latest peace deal is seen as the best hope to stop fighting that has killed over 5,480 people since April but scepticism is high after previous truces collapsed.
Poroshenko has said that he will introduce martial law across the whole territory of Ukraine if the ceasefire breaks down.