DONETSK, Ukraine — A top rebel leader announced Saturday that the rebel stronghold of Donetsk is surrounded by Ukrainian government troops and his forces were willing to accept a cease-fire in order to stave off a humanitarian catastrophe.

There was no immediate government response to the statement from Aleksandr Zakharchenko, the so-called prime minister of the Donetsk separatists.

Russia, which the Ukrainian government in Kiev and Western countries allege is supporting the rebels, has called repeatedly for a humanitarian mission into eastern Ukraine. But Kiev and the West suggest that could be just a pretext to send in Russian forces — and say some 20,000 Russian troops are just across the border.

The rebel leader's comments could be aimed at increasing the international pressure to allow in a Russian mission.

Conditions in Donetsk, the largest rebel-held city, were clearly deteriorating Saturday. The thunder of artillery reverberated and the streets of the city, home to nearly a million people before some 300,000 fled the conflict, were nearly empty of cars and pedestrians. Most stores were closed.

At least one person was killed and 18 wounded in shelling Saturday that hit about 30 apartment blocks, city council spokesman Maxim Rovinsky said.

"The situation is getting worse with every hour," he told The Associated Press, adding that about 2,000 residential buildings had no electricity.

Explosions were also heard Saturday on the northern outskirts near Donetsk's airport.

Ukrainian officials have consistently denied that their forces are shelling civilians, but the rebels dismiss that and claim the government is aiming to blame the insurgents for the increasing death and destruction.

Some say both sides are to blame.

"We're afraid of the Ukrainian army, which is firing on the city, and of the rebels of the Donetsk People's Republic, who are robbing and killing civilians," said Dmitry Andronov, a 47-year-old resident.

Zakharchenko's statement that the city was surrounded came hours after the rebels' top commander said Ukrainian forces had seized a key town, Krasnyi Luch, and effectively cut off Donetsk and nearby territory from the rest of the rebel-held east.

"The Donetsk-Horlivka group of the fighters of Novorossiya is completely surrounded," Igor Girkin said on a rebel social media page. Novosrossiya, or "New Russia," is a term widely used by the rebels for the eastern area that seeks independence from the government in Kiev. Horlivka, where rebels and Ukrainian forces are also fighting, is 30 kilometers (20 miles) north of Donetsk.

A spokesman for the Ukrainian military operation, Andriy Lysenko, told reporters Saturday that he could not confirm that the town was under government control.

Concerns are rising about a looming humanitarian catastrophe in the rebel east's second-largest city of Luhansk, where fighting has been heavier and more prolonged. A map released by the Ukrainian military shows Ukrainian forces near the outskirts of Luhansk on three sides, with an opening to other rebel-held territory only at the south.

Russian news agencies quoted Luhansk authorities as saying Saturday that the city has been without water and electricity for a week and most of its stores are closed.

The International Committee of the Red Cross said it is stepping up work to alleviate the crisis in eastern Ukraine but warned that any Red Cross aid convoy "will be taken in strict adherence to our fundamental working principles of neutrality, impartiality, and independence."

The deputy head of the Ukrainian presidential administration, Valeriy Chalyi, claimed Saturday that Russian forces wanted to enter Ukraine under the guise of a humanitarian mission but Ukraine had blocked the move.

Kremlin spokesman Dmitry Peskov denied the claim, saying "there was no attempt by Russian soldiers at penetration," according to Russian news agencies.

But he reiterated Russia's call for humanitarian action, saying "this catastrophe now is the No. 1 theme for discussion."