(Adds phone calls between Obama and Merkel, and Kerry and Lavrov; in paragraphs 8, 10-11)
KIEV, Aug 9 (Reuters) - Pro-Russian separatists said on Saturday 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 in Donbass," Alexander Zakharchenko, prime minister of the self-proclaimed Donetsk people's republic, said in a statement, referring to the area of eastern Ukraine where combat is being waged.
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.
Ukrainian officials have said they are ready to agree 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.
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, U.S. 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, according to a statement from Cameron's office.
Russian Foreign Minister Sergei Lavrov, in a phone call with U.S. Secretary of State John Kerry, called for "urgent measures for preventing an impending humanitarian catastrophe in south eastern 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 U.S. State Department official said.
Ukraine has made several statements about Russian aggression during months of conflict with separatists on its eastern border with Russia that it says are backed by Moscow, none of which have been independently verifiable.
Ukraine says it has been gradually tightening the noose around the rebels, who have now been pushed back into their redoubts of Donetsk and Luhansk on the border.
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.
It was not immediately clear what convoy Poroshenko's aide was referring to.
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 huge military convoy accompanied by Russian soldiers and equipment was moving towards the Ukrainian border, allegedly by agreement with the Red Cross," said Valery Chaly, deputy head of Poroshenko's administration.
No one at the Red Cross was immediately available to comment.
"A humanitarian column with 'peacekeepers' was to enter the territory of Ukraine, clearly to provoke a full-scale conflict," he said, according to Ukraine's presidential press service.
Chaly said Poroshenko held urgent talks with his security chiefs and world leaders, though he did not specify which ones.
Separately, Foreign Minister Pavlo Klimkin said he had called his Russian counterpart Sergei Lavrov who had assured him the convoy would be stopped.
"As of now, the danger of provocation has been removed, but operational staff continue to work," 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.
"The (Ukrainian) National Guard probably have to report about their achievements in the field, so they pretended they have some," she said.
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."
Ukraine and the West see a growing danger of a Russian invasion under the guise of a peacekeeping mission. Kiev says any such mission would be perceived as direct aggression.
The head of NATO, Anders Fogh Rasmussen, this week called on Russia to pull its troops back from the Ukrainian border and warned further intervention would mean greater isolation from the rest of the world.
The head of the U.S.-led alliance said Russia had massed about 20,000 troops near Ukrainian border, very close to the regions where Ukrainian government forces are fighting pro-Russian rebels.
Ukrainian officials say that frequent Russian military exercises near the border complicated the situation. On Saturday a Ukrainian military spokesman said the move was not a "stage in de-escalation of the situation near the border".
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. (Reporting by Pavel Polityuk in Kiev; Additional reporting by Gabriela Baczynska, Polina Devitt, Alexei Anishchuk and Jason Bush in Moscow and Mohammad Zargham in Washington; Writing by Richard Balmforth in Kiev; Editing by Sophie Hares and David Gregorio)