DONETSK, Ukraine — Ukraine’s rebels are surrounded and ready to agree to a cease-fire to prevent a ‘‘humanitarian catastrophe,’’ the insurgents’ new leader said Saturday as conditions deteriorated in the rebel stronghold of Donetsk, artillery thundering through deserted streets.
There was no immediate government response to the cease-fire statement. Ukrainian troops have made steady advances against the rebels in recent weeks.
‘‘We are prepared to stop firing to bar the spread of the scale of the humanitarian catastrophe in Donbass (eastern Ukraine),’’ Aleksandr Zakharchenko, called the prime minister of the Donetsk separatists, said in a statement.
His motive for offering a cease-fire was not clear but his comments could be aimed at increasing the pressure on Ukraine to allow in a Russian aid mission.
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 Russian forces into the region — and say about 20,000 of them have gathered across the border.
Ukrainian President Petro Poroshenko issued a statement late Saturday saying that Ukraine is prepared to accept humanitarian assistance in eastern Ukraine. But he said the aid must come in without military accompaniment, it must pass through border checkpoints under Ukrainian control, and the mission must be international in character.
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.
Artillery reverberated Saturday across Donetsk, home to nearly 1 million people before 300,000 fled the conflict.
‘‘The situation is getting worse with every hour,’’ Donetsk City Council spokesman Maxim Rovinsky said.
At least one person was killed and 18 wounded in shelling that hit about 30 apartment blocks Saturday in Donetsk, he said, adding that about 2,000 residential buildings had no electricity.
City streets were nearly empty of cars and pedestrians and most stores were closed. Explosions were also heard 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. Ukraine says the rebels have deliberately put rocket launchers in populated areas.
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, effectively cutting 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.
Novorossiya, 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 20 miles north of Donetsk.
A spokesman for the Ukrainian military operation, Andriy Lysenko, told reporters Saturday he could not confirm that Krasnyi Luch was under government control.
Concerns were also rising about a possible humanitarian catastrophe in the rebel’s second-largest city of Luhansk, where fighting has been heavier and more prolonged.