The ceasefire is seen as a first step in a peace plan aimed at ending 10 months of conflict in eastern Ukraine.
Within two hours into the ceasefire, which came into effect on Saturday at midnight local time or 2200 GMT, Kiev reported attacks by pro-Russian separatists in the Luhansk area.
"Pro-Russian militants used artillery, mortars and grenade launchers to attack the Ukrainian positions ... near Zolote, Sanzharivka, Popasna, Chornukhine by 2am," said tweets by Ukrainian army early on Sunday.
Meanwhile, rebels accused the Ukrainians of deploying artillery shortly after midnight, the AP said.
Anxiety remains high that unrest could be sparked anew by rival claims to Debaltseve, a strategic railway hub now controlled by the government.
On Saturday, intense fighting persisted around Debaltseve, in the eastern part of Ukraine, which has been besieged by separatist forces.