Ukrainian President Petro Poroshenko has said he is ready to consider allowing humanitarian assistance into the rebel-held area of eastern Ukraine.But he said any such mission must be international and unarmed and only enter via Ukrainian-manned checkpoints.
Russia has repeatedly called for a humanitarian mission but the West fears it could use it to send in troops.
Meanwhile, pro-Russian separatists have called for a ceasefire in Donetsk to avert a “humanitarian catastrophe”.
Rebels said the Ukrainian army had taken the key town of Krasnyi Luch and encircled Donetsk.
Reports from the city of Luhansk, second only to Donetsk in its importance to the rebels, also suggested living conditions were dire.
The Luhansk city council reported on its website (in Russian) on Saturday that the city of 425,000 people had been without electricity and power for a week.
Parts of the city were still being bombarded and most shops were shut.
An estimated 1,500 people have been killed since pro-Russian rebels stormed eastern cities in April and took over government buildings in a bid for independence.
The government stepped up operations to retake rebel-held areas following the election of Mr Poroshenko as president in June.
Russia – which annexed Crimea from Ukraine in March – has been widely accused of supporting and covertly supplying the rebels, a claim it strongly denies.
“We are ready to accept humanitarian aid if the mission is an international one, without any military escort and if it passes through border checkpoints controlled by Ukrainian guards,” President Poroshenko told German Chancellor Angela Merkel in a phone conversation, according to a statement issued by his office.
In Washington, the White House said President Barack Obama and Chancellor Merkel agreed that any Russian intervention in Ukraine was unacceptable and would violate international law.
The deputy head of Ukraine’s presidential administration, Valeriy Chalyi, said on Saturday that Russian troops wanted to enter Ukraine under the guise of a humanitarian mission but Ukraine had blocked the move.
Kremlin spokesman Dmitry Peskov denied the claim but he reiterated Russia’s call for humanitarian action, saying; “This catastrophe now is the number one theme for discussion.”
As fighting on the ground intensified, Aleksandr Zakharchenko, the self-styled prime minister of the Donetsk separatists, said in a statement on a rebel website: “We are prepared to stop firing to bar the spread of the scale of the humanitarian catastrophe in Donbass (eastern Ukraine).”
Donetsk city council spokesman Maxim Rovinsky told AP news agency that the situation is “getting worse with every hour”.
He said at least one person was killed and 18 wounded when shells hit apartment blocks on Saturday.
City streets were mostly deserted and most stores were closed. Explosions were also heard near Donetsk’s airport.
Resident Dmitry Andronov said: “We’re afraid of the Ukrainian army, which is firing on the city, and of the rebels… who are robbing and killing civilians.”