KIEV, Ukraine — Ukraine’s military announced on Thursday that it would begin withdrawing some heavy artillery from areas bordering separatist-held territory in the country’s southeast under a cease-fire agreement negotiated this month.

The announcement followed the separatists’ capture of the strategic town Debaltseve last week in an onslaught that President Petro O. Poroshenko called a “brutal violation” of the cease-fire agreement signed just days earlier in Minsk, Belarus.

Though the deal appeared in tatters, Thursday’s statement reaffirmed the government’s support for the cease-fire, which could provide a road map to ending a conflict that has left nearly 6,000 dead since last April. Ukraine’s military also reported Thursday that no servicemen had been killed or wounded for a second straight day along the so-called “line of confrontation” between Ukrainian forces and the Russian-backed rebels.

“Today, Ukraine begins the withdrawal of 100-millimeter guns from the dividing lines” of the conflict, a government statement on the military’s official website said, adding that the withdrawal should be monitored by the Organization for Security and Cooperation in Europe.