MOSCOW — Leaders of a Russian-backed rebel movement in eastern Ukraine claimed on Friday to have captured the Donetsk city airport, a symbolically important and long-sought prize, although central government officials denied this was the case.

A senior leader for the rebels, the pro-Russian Donetsk People’s Republic, described the fight as the start of a new offensive to push Ukraine out of the east.

Despite a cease-fire that was signed on Sept. 5, the sides have fought in the rubble of the airport terminals for months. The rebels have repeatedly claimed to have captured the site, even though Ukrainian forces have been able to hold onto pockets inside the terminal. A major escalation in shelling preceded the latest claim.

If the claim is true, it would signal the first significant territorial advance by the rebels since the signing of the cease-fire pact.