An elderly man and woman died after Grad missile fire hit the town of Popasna in the Lugansk region some 20 minutes after the truce came into force at 2200 GMT Saturday (0900 AEDT Sunday), local governor Gennadiy Moskal said.
Sunday's firing came from an area that Kiev says is under the command of a renegade group of Cossack fighters who insist they will not obey rebel chief commands to cease fire.
Ukraine's military said its forces had been fired at 10 times overnight but that there had been no incidents reported since 1200 AEDT Sunday.
However, they reported that rebels were still trying to occupy the village of Chornuhine around the key strategic government-held town of Debaltseve.
Debaltseve is seen as the more likely potential flashpoint for violence, as pro-Russian rebels battled fiercely to surround Ukranian forces in the hours leading up to the truce.
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