"The 'regime of silence' is being followed on the majority of the territory of the republic, the situation is generally calm. Separate violations by the Kiev army have been registered near the Debaltsevo pocket," deputy head of the DPR militia Eduard Basurin said, as quoted by the Donetsk News Agency.
Kiev military spokesman said earlier in the day that no shelling by the independence supporters has been registered since 03:00 local time (01:00 GMT).
French Foreign Minister Laurent Fabius told iTele television Sunday that the warring sides in Ukraine were mostly adhering to the ceasefire, despite particular breaches.
The government forces and independence supporters have accused each other of several violations since the ceasefire took effect on Sunday midnight Kiev time [22:00 GMT].
Earlier Kiev forces shelled the territory controlled by independence supporters in Donbas twice since the ceasefire took effect at midnight, the independence supporters headquarters said Sunday.
The truce deal between the Ukrainian troops and pro-independence forces was brokered by the leaders of France and Germany and Russia on February 12 in Minsk. The conflict, which started in April last year, has killed over 5,400 people, according to UN estimates.