Pro-Russian separatists have said they were ready for a ceasefire with the Kiev government after increasing gains by Ukrainian forces against rebel forces.
"We are ready for a ceasefire to prevent the proliferation of a humanitarian disaster...," Alexander Zakharchenko, prime minister of the self-proclaimed Donetsk People's Republic, said in a statement on Saturday.
He warned that Donetsk, the main industrial hub which is the centre of the rebel resistance, faced a lack of food, water, and electricity, but said the rebels were ready to defend the city of around one million people.
"In the event of a storm of the city the number of victims will increase by magnitude. We have no humanitarian corridors. There is no supply of medicines ... food supplies are nearing their end," he said.
We are ready for a ceasefire to prevent the proliferation of a humanitarian disaster.
Ukrainian officials say they are ready for a ceasefire but on condition the rebels surrender their arms.
The office of Ukrainian President Petro Poroshenko was unavailable for immediate comment on Zakharchenko's statement, Reuters news agency reported.
Earlier, Kiev said it had headed off an attempt by Russia to send troops into Ukraine under the guise of peacekeepers with the aim of provoking a large-scale military conflict, a statement Moscow dismissed as a "fairy tale".
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 authorisation 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, according to a statement from Cameron's office.
Russian Foreign Minister Sergei Lavrov, in a phone call with US Secretary of State John Kerry, called for "urgent measures for preventing an impending humanitarian catastrophe in southeastern regions" of Ukraine, the Russian foreign ministry said.
Kerry "conveyed that Russia should not intervene in Ukraine under the guise of humanitarian convoys or any other pretext of 'peacekeeping'," a senior US State Department official said.
Russia slams claims
A senior aide to Poroshenko said a large Russian military convoy had been heading for the border on Friday under a supposed agreement with the Red Cross, but had stopped after an appeal by Kiev to Russia.
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.
"A humanitarian column with 'peacekeepers' was to enter the territory of Ukraine, clearly to provoke a full-scale conflict," said Valery Chaly, deputy head of Poroshenko's administration.
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"As of now, the danger of provocation has been removed," Chaly said.
Maria Zakharova, a spokeswoman for the Russian foreign ministry, dismissed Chaly's statement as untrue. "Each time Kiev is more and more inventive in creating fairy tales," she said, noting special protocols had to be completed before Russian troops could be sent abroad.
Dmitry Peskov, the spokesman for Russian President Vladimir Putin, said by phone: "We don't know what [the Ukrainians] are talking about because nothing like that happened."
Ukrainian officials say that frequent Russian military exercises near the border complicated the situation. Ukraine and its western allies accuse Russia of orchestrating the revolt and arming the rebels, who have declared independent "people's republics" in the two main industrial regions. Moscow denies involvement.