Fighting raged in the city of Donetsk Sunday as government forces continued to close in on the rebel stronghold, and pro-Russian insurgents backed away from an unconditional cease-fire offer that they announced just the day before.

With a string of military successes and broad support for its campaign from the West and most of its domestic base, Kiev has taken a hard line against the rebel forces and promised that it will relent only when the separatists surrender. Donetsk remained a ghost town Sunday, with few civilians daring to venture outside as explosions rang out every few minutes and burnt-out buses and buildings smoldered from the night before.

In a statement Saturday, newly-elected rebel leader Aleksandr Zakharchenko appeared to call for a cease-fire without placing any preconditions. But Sunday, rebel spokeswoman Elena Nikitina repeated the rebels’ earlier stance, saying talks could begin only if the Ukrainian army withdrew from the region — something Kiev is unlikely to do.

Andrii Lysenko, spokesman for Ukraine’s National Security and Defense Council, said that the only way for the rebels in Donetsk to save their lives would be to “lay down their arms and give up.” He said the Ukrainian side hadn’t seen the rebels show any real willingness to cooperate.

Lysenko said that the military’s recent successes in encircling Donetsk had bred “panic and chaos in the ranks of the rebels” and said that the Kiev government had information about rebels “deserting their posts en masse.”

Conditions were clearly deteriorating in Donetsk, the largest rebel stronghold in eastern Ukraine. According to city council spokesman Maxim Rovinsky, at least one person was killed and 10 injured in shelling overnight, as more than 10 residential buildings, a hospital and a shop were heavily damaged in the fighting.

Rovinsky estimated that 100,000 people had left the city of 1 million in the past week alone — adding to the 300,000 already estimated to have fled. He said that at least 10,000 people were without electricity and that the local government was working hard to preserve access to gas, electricity and phone service and “avoid a humanitarian crisis.” More than 1,300 people have died in the conflict since April, according to a U.N. estimate.

Zakharchenko’s apparent call for a cease-fire Saturday was met with support from Russia, where Foreign Minister Sergei Lavrov was quoted by the news agency ITAR-TASS as saying that a truce was “not only possible, but necessary.”

“We believe the question is urgent and there can be no delay, and the issue is under the control of the Russian president,” he said. Lavrov said Russia was reaching out to the Red Cross and the United Nations to discuss the possibility of delivering humanitarian aid to the region.

However, the rebels’ request was met warily by officials in Kiev and in the West. Those leaders expressed concern that the move could be aimed at increasing international pressure on Ukraine to allow in a Russian aid mission. The West says that could be used as a pretext to bring Russian soldiers into Ukraine — and that 20,000 of them are massed near the border with Ukraine.

Ukrainian President Petro Poroshenko and Western leaders have repeatedly accused Russia of providing arms and expertise to the rebels, something Russia denies.

He issued a statement late Saturday saying that Ukraine was prepared to accept humanitarian assistance in eastern Ukraine. But he said the aid must come in without military assistance, pass through border checkpoints under Ukrainian control and be an international mission.

Poroshenko said he and German Chancellor Angela Merkel discussed German participation in such a mission.

In Washington, the White House said President Obama and Merkel agreed that any Russian intervention in Ukraine was unacceptable and would violate international law. Obama and British Prime Minister David Cameron, meanwhile, “expressed grave concern about reports that Russian military vehicles have crossed the border into Ukraine and that Russian armed forces are exercising for a ‘humanitarian intervention,’ ” according to Cameron’s office.

— Associated Press