"We declare that we will guarantee the safety of international experts on the scene as soon as Kiev concludes a ceasefire agreement," the self-proclaimed Donetsk People's Republic's deputy premier Andrei Purgin said in a statement.
He urged Kiev to "immediately conclude such an agreement" with the rebels.
Failure to do so would give the impression that the government is made up of "dangerous lunatics, bloodthirsty maniacs (who are) dangerous not only for the residents of Donbass but also for the world community", Purgin warned.
Purgin's statement came as the international community piled pressure on Russia to get the Moscow-backed rebels to grant investigators full access to the crash site of the Malaysian MH17 jet.
International anger towards Russia mounted Sunday after armed separatists denied full access to inspectors and rebels were accused of tampering with evidence at the crash site of the Malaysian MH17 jet in eastern Ukraine.
Outraged world leaders demanded Russia's full cooperation into the shooting down of the Kuala Lumpur-bound flight from Amsterdam with 298 people from a dozen countries on board, as Ukraine warned rebels were "hours away" from removing key evidence across the Russian border.
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Liu Ling, whose husband was onboard Malaysia Airlines Flight MH370 which disappeared on March 8, cries during an interview with Reuters. Liu said she "felt more terrible after hearing about Thursday's incident and is now more certain that MH370 did not crash because the downed MH17 showed how a crash should look like". (Reuters photo)
US Secretary of State John Kerry led the global chorus of disapproval by telling Russian Foreign Minister Sergei Lavrov, during a telephone call, that Washington was "deeply concerned" investigators were denied "proper access" to the crash site for a second consecutive day.
"The United States is also very concerned about reports that the remains of some victims and debris from the site are being tampered with or inappropriately removed from the site," the State Department said.
Kerry was backed by leaders from Britain, the Netherlands, Malaysia, Australia and France -- as well as Ukraine -- in calling on Russian president Vladimir Putin to cooperate more in helping an international investigation begin and recover the bodies of the 298 victims.
Emergency workers load the body of a victim on a truck at the crash site of Malaysia Airlines Flight 17 near the village of Hrabove, eastern Ukraine. (AP photo)
There was growing concern about the whereabouts of some of the bodies which had been removed from the crash site, while others were left lying in field in the rural part of eastern Ukraine where the Boeing 777 jet was brought to ground.
British Prime Minister David Cameron, writing in the Sunday Times newspaper, said: "Russia can use this moment to find a path out of this festering, dangerous crisis. I hope it will do so. But if that does not happen then we must respond robustly."
He called for tougher European action against Moscow. "If President Putin does not change his approach on Ukraine, then Europe and the West must fundamentally change our approach to Russia."
Dutch Prime Minister Mark Rutte -- his tiny nation mourning the loss of 192 compatriots -- said he had called on Russian President Vladimir Putin during a "very intense" conversation to "take responsibility" for a credible investigation.
Rutte also backs stronger European action against Moscow.
At the crash site, gunmen showed few signs of being ready to cooperate with an investigation that could blame them for blowing apart the Boeing 777 jet.
International monitors were met on Saturday by Kalashnikov-wielding militias who allowed them access to only the outskirts of the field -- its swaying sunflowers hiding dismembered remains of charred and decomposing bodies of victims whose lives were cut short on Thursday.
A picture taken on July 19, 2014 shows the wreckage of Malaysia Airlines flight MH17 two days after it crashed in a sunflower field near the village of Rassipnoe, in rebel-held east Ukraine. (AFP photo)
The Ukrainian government issued a furious statement declaring that "terrorists with the support of Russia are trying to destroy proof of this international crime".
Kiev said armed fighters were hours away from loading vital clues aboard trucks that would be rushed across the Russian border before a full team of experts inspected the expansive site where remains of flight MH17 hit the ground.
Missing black boxes
Malaysia's transport minister expressed alarm before boarding a flight to Kiev over "indications that vital evidence has not been preserved in place".
"One of the crucial questions is the fate of the black boxes," said Organisation for Security and Cooperation in Europe spokesman Michael Bociurkiw.
He said the Vienna-based group's monitoring team on the ground had been "unable today, for the second day, to gain any answers to that question".
France's President Hollande, following a phone call with his Ukrainian counterpart Petro Poroshenko, said the two had agreed "on the importance of establishing the facts" of what happened to the doomed plane.
People arrange candles to offer prayers for the victims of the Malaysia Airlines Flight 17, at a shopping mall in Petaling Jaya, near Kuala Lumpur, Malaysia. (AP photo)
The head of the self-proclaimed Donetsk People's Republic into whose airspace the doomed jet strayed to avoid bad weather said his men had never recovered the data recorders or tampered with evidence.
But he found the Kremlin's verbal backing eroding as the day wore on and global pressure on Putin mounted.
After their phone call Kerry and Lavrov said that "material evidence, including black boxes" must be immediately handed over to inspectors.
The diplomatic wrangling was accompanied by uninterrupted fighting across Ukraine's eastern rustbelt -- a Russia-speaking region of seven million people who largely view the more nationalistic west of the splintered country with mistrust.
Ukrainian forces reported taking full control of the main airport of the neighbouring separatist stronghold of Lugansk and launching all-out offensives against two nearby towns.
Government troops said they had also established full control of Donetsk airport for the first time since it was seized at the end of May in a bloody raid that saw militias lose more than 40 fighters -- most of them Russian nationals.
Kiev said the latest clashes killed five soldiers and wounded another 20.
US President Barack Obama and major world leaders now agree that the Malaysia Airlines jet was blown out of the sky at 33,000 feet (10,000 metres) by a sophisticated surface-to-air missile fired from rebel-controlled territory.
Kiev has gone a step further by accusing militias of using a Russian-supplied Buk system to down the jet after confusing it with a Ukrainian military transporter.
Ukraine has released recordings of what it said was an intercepted call between an insurgent commander and a Russian intelligence officer as they realised they had shot down a passenger jet.
But Putin has blamed the tragedy on Kiev's three-month military operation and said its new leaders were solely responsible for security across the strategic nation.
Moscow has also drawn some governments' ire by questioning why the packed jet was flying over a combat zone in the first place.
The plane's downing came less than a day after the United States unleashed punishing sanctions against some of Russia's most important energy and military firms -- most of them with links to Putin -- and urged more hesitant European leaders to follow suit.
"I think that this certainly will be a wake-up call for Europe and the world that there are consequences to an escalation of the conflict in eastern Ukraine," Obama said in a special address.
EU reviews Russia ties
The European Union -- many of its member states dependent on Russian gas -- took the far less punitive step on Friday of curbing some future investments in Russia and leaving the option open for broader sanctions.
Putin rejects all charges of providing either funding or military support to the insurgents in order to punish the new pro-Western leaders in Kiev.
Rebel commanders have also denied being in possession of any functioning Buk systems.