Under a near-constant barrage of artillery fire, Ukrainian forces and separatist rebels fought fierce street battles Tuesday for control of the strategic railway hub of Debaltseve, a battle impeding implementation of a peace plan.

Ukraine denied rebel claims to have taken control of the town but acknowledged the separatists had seized parts of it. The battle came despite a weekend cease-fire that obliged both sides to start moving back their big guns Tuesday.

A key railroad junction between the separatist east’s two main cities, Donetsk and Luhansk, Debaltseve has been the focus of fighting over the past two weeks and capturing it would be a prize for the Russia-backed rebels.

The defense ministry said street battles continued there Tuesday and government soldiers had been ambushed and taken prisoner, but gave no details on how many were seized. Rebel spokesman Eduard Basurin said hundreds of Ukrainian soldiers had surrendered in Debaltseve.

The Ukrainian presidential office called on the European Union and NATO to condemn the Russia-backed rebels for violating the cease-fire brokered by the leaders of Ukraine, Russia, Germany and France last week.

The war in eastern Ukraine has already killed more than 5,600 people and displaced more than a million, the United Nations said Monday. It has also left the country’s industrial heartland in ruins.

On Tuesday, as the deadline passed for both sides to begin pulling back heavy weapons from the front line, rebel commander Vladimir Kononov said on Russian television that most of Debaltseve was under separatist control and urged the Ukrainian troops to give up.

“Their only choice is to leave behind weaponry, lay down arms and surrender,” he said.

Rebel official Basurin announced in a televised briefing that the separatists “will take the initiative” and begin to pull back their big guns from some sections of the front line. He did not provide a timeline.

The Ukrainian government, however, insisted on a comprehensive cease-fire before pulling back its weaponry, and government positions kept up a near-constant artillery bombardment.

“The situation in Debaltseve is extremely complicated and is changing by the hour,” Ukrainian military spokesman Andruy Lysenko said late Tuesday. “Several groups of the enemy have burst into the city.”

Fighting has stopped or subsided in some parts of war-torn eastern Ukraine, however. Basurin said Tuesday the separatists had not seen any violations of the cease-fire in the area around the rebel stronghold of Donetsk since 8 p.m. Monday.

The continued fighting comes as concern remains about whether the United States will decide to send lethal weapons to Ukraine.

Russian President Vladimir Putin said Tuesday at a news conference in the Hungarian capital, Budapest, that, “according to our information, these weapons are already being delivered.” He did not elaborate but said the consequences of new weapons for Ukraine would be “the number of victims, of course, can increase. But the result will be the same as it is today. This is unavoidable.”