Artillery shells slammed into the outskirts of the Ukrainian city of Donetsk on Sunday as government forces tightened the noose around the rebel-held redoubt and called on pro-Russian separatists to surrender.
To the east of Donetsk, government forces and the separatists were fighting for control of the town of Krasny Luch, a rail and road junction through which Kiev says the rebels are receiving supplies of Russian military equipment.
Talk of a ceasefire, a possibility raised by a separatist leader on Saturday, evaporated as Kiev government forces kept up an offensive to crush the rebels.
Ukrainian military spokesman Andriy Lysenko said if the rebels wanted a ceasefire this meant "raising white flags and putting down their guns".
There would be no truce while the Ukrainian army continued "punitive" military action, the rebels retorted in a statement.
Donetsk, a major industrial hub in Ukraine's Russian-speaking east, resonated with the crash of shells on its outskirts for about eight hours up to mid-day on Sunday, a Reuters witness in the town said.
In the city's northern district of Putilovka, a building housing the offices of Ukrtelecom telecommunications company was ablaze, apparently hit by a shell. Residents had come out to watch, while one man was putting up corrugated metal to protect the windows of his home.
'Tightening the circle'
Lysenko said in the past 24 hours, the military had "continued successful offensive operations, considerably tightening the circle around the capital of the Donbass, Donetsk". He added: "The (separatist) fighters are in panic and chaos. There are numerous cases of desertion among the terrorists."
Neither he nor the rebels gave any indication of casualties in the fighting over the weekend.
A statement on the Facebook page of rebel commander Igor Girkin, known as Strelkov (The Shooter), said: "They have been bombing all morning. There are explosions, some close, some far off. There is news coming in all the time by phone. Just now, we had a fire near hospital No 18, a woman has been killed."
Accusing the Ukrainians of maintaining "punitive" operations that endangered the people in Donetsk and threatened a humanitarian catastrophe, a later rebel statement said: "As long as the Ukrainian army is continuing military action there can be no ceasefire."
Ukraine and its Western allies accuse Russia of orchestrating the separatist revolt which erupted in April after Russia's annexation of Ukraine's Crimea peninsula. It says Russia is funnelling tanks and missile systems to the rebels, who have declared independent "people's republics" in the two main industrial regions. Moscow denies involvement.
Donetsk, a once bustling metropolis of nearly one million people, is facing an increasing shortage of food, water and electricity. Few people are on the streets, though groups of armed separatist fighters can be seen, and few cars. Most people are staying indoors or have left the city for the countryside.
Most shops are closed but the municipal authorities said bakeries were still producing bread despite a lack of electricity. Fuel supplies had run out and few chemists are operating. Banks are closed and pensions and social allowances are not being paid.
Repeating charges of violations of Ukrainian airspace by Russian warplanes, something denied by Moscow, Lysenko said a battle was now underway for Krasny Luch, a junction midway between the two rebel-held cities of Donetsk and Luhansk and a staging post for supplies of Russian military equipment to the rebels, Kiev says.
"If we take this, it will guarantee we can block a route through which the terrorists are receiving aid. Fighting is going on there - very hot fighting," Lysenko said.
"Our forces are doing all they can to take it (the town) as quickly as possible," he said.
Though all sides recognise the seriousness of the humanitarian situation in eastern Ukraine, Kiev and its Western allies suspect Russia could use the situation to move its forces into the country.
Kiev said on Saturday it had headed off, by diplomatic means, an attempt by Russia to send troops into Ukraine under the guise of peacekeepers accompanying a humanitarian convoy sanctioned by the Red Cross. Moscow dismissed the allegation as a "fairy tale".
Ukraine and Western allies accuse Russia of orchestrating the revolt and arming the rebels. Moscow denies involvement.
The geopolitical tussle over the future of the ex-Soviet country of 46 million people has grown sharper since the July 17 downing of a Malaysian airliner in the eastern Ukraine conflict zone, with the deaths of all 298 passengers and crew.
Kiev and its Western allies have laid the blame for the attack at the door of the rebels. The separatists and Russia say flight MH17 was downed as a result of Ukraine's military offensive against the rebels.
Russian Foreign Minister Sergei Lavrov said on Sunday Moscow was in talks with Kiev, the International Committee of the Red Cross and the United Nations on sending humanitarian aid to eastern Ukraine.
The White House said that during a call on Saturday, US President Barack Obama and German Chancellor Angela Merkel "agreed that any Russian intervention in Ukraine, even under purported 'humanitarian' auspices, without the formal, express consent and authorization of the government of Ukraine is unacceptable, violates international law, and will provoke additional consequences."
Obama and British Prime Minister David Cameron also discussed the crisis and said tougher sanctions should be imposed on Russia if it sends troops into Ukraine.
On Friday, Russia's defence ministry said it had finished military exercises in southern Russia, near the Ukrainian border, which the United States had criticised as provocative.