MOSCOW — Ukraine and one of two Russian-backed rebel groups fighting in eastern Ukraine have pledged to recommit to a cease-fire along one portion of the front, European monitors said on Tuesday, in the first new step toward a diplomatic settlement of the conflict in months.

Under the agreement announced by the Organization for Security and Cooperation in Europe, the Ukrainian military and Luhansk People’s Republic agreed to order a cease-fire along the front starting Friday, and then to pull heavy weaponry from a buffer zone starting Saturday.

Both Ukraine and the Russian-backed rebel groups had committed to the same terms under a deal also signed by Russia on Sept. 5. But cease-fire violations have run into the dozens every day since, so that about a quarter of the estimated 4,300 civilians and soldiers killed in eastern Ukraine during the war died after the agreement was signed.

The O.S.C.E. announced the new cease-fire in the Luhansk region late Monday, after talks over the weekend. Some points remained to be ironed out, it said.