LUHANSKOYE, Ukraine — The first day of a cease-fire in eastern Ukraine was marred by deadly artillery fire on Sunday, and both the Ukrainian military and Russian-backed separatists accused each other of violating the new accord.

Some lingering violence was expected, given the recent intensity of the combat, yet over all, Ukrainian officials said, the accord reached last week was holding.

A lull after the midnight cease-fire deadline, however, was followed Sunday morning by a resumption of shelling near the disputed town of Debaltseve, where the fate of about 8,000 Ukrainian soldiers remained unresolved in the negotiations leading to the cease-fire.

By midday, shells and rockets were flying in both directions over the front line about nine miles north of the besieged town.