The Ukrainian military said on Monday that it would delay pulling its heavy weapons back from the front lines, despite an apparent agreement between the army and the rebels over the weekend to start the withdrawal on Sunday. The military said separatist forces fired artillery volleys at two villages in the northern part of the Donetsk region on Monday while continuing to assault the fortifications protecting the port city of Mariupol on the Sea of Azov.

Ukraine will withdraw its artillery only after calm has prevailed on the front lines for at least 24 hours, the chief spokesman for the general staff, Vladislav Seleznyov, said at a briefing in Kiev, the capital. “Because the militants continue to shell the positions of our military, it’s impossible for now to speak of pulling back heavy weapons,” Mr. Seleznyov said.

Col. Valentin Fedichiv, a deputy commander of military operations in the east, told Channel 5 television on Monday of another setback for the military: An American-supplied counter-battery radar system, which spots the source of incoming artillery fire, was lost in the hurried retreat from Debaltseve.

Colonel Fedichiv said that as officers in the town prepared for the retreat, they rigged explosives to destroy any major equipment that would have to be left behind, including armored vehicles and the radar system. “The last battalion had an order to blow up everything,” he told the television station. “We heard explosions, but the detonations may not have worked on all equipment.”

In Donetsk, the separatist government asked on Monday for a local cease-fire in the area of the city’s combat-ravaged airport, where they planned to use heavy construction equipment to move concrete rubble and unearth the bodies of soldiers who were crushed beneath.

Fierce fighting raged at the airport until late January, when the separatists succeeded in taking it by collapsing the upper floors of a building onto the government troops who were holding out on lower levels. The digging would be overseen by the Red Cross, according to a separatist statement.

The main rebel leader, Aleksandr V. Zakharchenko, who was wounded leading his troops in the battle of Debaltseve after signing the truce agreement in Minsk, issued a statement on Monday from the hospital where he was being treated, congratulating his followers on the martial holiday.

“Today, our opponents are negotiating with us, as they fear us and respect our strength,” he said. “This is, more than anything, thanks to you.”