Leaders of Britain, France, Germany and Australia have spoken to Russian President Vladimir Putin by phone late on Sunday, urging him to use his influence on the separatists to ensure the victims could be repatriated and international investigators could have full access to collect evidence.
They said European foreign ministers will be meeting in Brussels on Tuesday to consider further sanctions on Russia.
More than three days after the jetliner crashed, international investigators still had only limited access to the sprawling fields where the plane fell.
UN Security Council diplomats tweeted on Sunday that the council would vote on Monday afternoon on a draft resolution co-sponsored by Australia, France and Lithuania that would call for full access to the crash site and an independent investigation.
Diplomats met to discuss the language until after midnight Monday, after an emergency council meeting on the situation in Gaza.
Australian Prime Minister Tony Abbott, whose country lost 28 citizens in the tragedy, said Putin "said all the right things" during their telephone conversation about ensuring an international investigation into the disaster.
"I'm now going to try to ensure that as far as Australia humanly can, we insist upon these things happening," Abbott told Sydney Radio 2GB on Monday. "The site is being treated more like a garden clean-up than a forensic investigation, and this is completely unacceptable."
Russian officials have blamed Ukraine's government for creating the situation and atmosphere in which the plane was downed, but has yet to directly address the allegations that the separatists were responsible or were operating with technical assistance from Moscow.
In a statement posted on Monday on the Kremlin website, Putin said he supported an investigation of the scene by a "full team of experts" under the auspices of the International Civil Aviation Organisation, a UN agency.
Putin also lambasted nations that use the crash for "mercenary objectives". He didn't name any countries.
The 109-square-kilometer crash site, spread out on farmland and villages, looked dramatically different on Sunday, a day after armed rebels had stood guard while dozens of bodies lay in the summer heat.
The rebels were gone, and 192 bodies were loaded into the refrigerated train cars in the rebel-held town of Torez, 15km away.
The Ukrainian government said in a statement on its website that a second train with four refrigerator cars had arrived at Torez station.
Emergency workers, who the rebels have allowed to operate under their control, were searching the sprawling fields. Cranes moved pieces of the plane around, apparently to look for more bodies underneath.
By Sunday night, Ukraine's emergency services agency said the total number of bodies found was 251, with dozens of body parts.
Dutch Prime Minister Mark Rutte, whose country lost 192 citizens on the plane, told a news conference that repatriating the bodies was his "No. 1 priority".
He said all efforts were aimed at getting the train with the bodies to "territory controlled by Ukraine", adding that a Dutch military plane was being sent to Kharkiv to set up a co-ordination center.
Michael Bociurkiw, a spokesperson for the Organisation for Security and Co-operation in Europe, said reports from the group's investigators in Ukraine suggest some bodies were incinerated without a trace.
"We're looking at the field where the engines have come down. This was the area which was exposed to the most intense heat. We do not see any bodies here. It appears that some have been vaporised," he said from the crash site.
Rebel leader Alexander Borodai denied the rebels were trying to tamper with evidence, saying the bodies would be turned over to a team of Malaysian experts he was expecting.
A group of investigators that included Malaysian officials was in Kiev, but said they wouldn't go into rebel-held areas until they get better assurances about security.
The Ukrainian government, which has responsibility for the investigation, has also asked for help from the International Civil Aviation Organisation and Eurocontrol, a European air traffic safety organisation.
Borodai insisted the rebels have not interfered with the investigation, and said he would turn over the plane's flight data and cockpit voice recorders, or "black boxes", as well.
"The bodies will go nowhere until experts arrive," Borodai said in the rebel-held city of Donetsk.
But it was clear that the rebels were interfering in the investigation.
Pressure on Putin
Lyubov Kudryavets, a worker at the Torez morgue, said that on the evening the plane went down, a resident brought in the bloodied body of a child, about 7 or 8 years old. On Saturday, militiamen came to take away the body away, she said.
"They began to question me: 'Where are the fragments of rocket? Where are the fragments from the plane?'" Kudryavets said. "But I didn't have any wreckage. ... I swear."
Experts said that even if investigators are granted access now, it might be too late.
"Even without any deliberate attempt at a cover-up, the crash site is already compromised in forensic terms," said Keir Giles, an associate fellow at the Chatham House think tank.
"A reconstruction of the aircraft fuselage and wings would give a picture on how the missile struck and what kind it was. If any aircraft parts have already been removed ... this compromises the objectivity of the investigation."
On the diplomatic front, Western leaders stepped up the pressure on Putin. The leaders of France, Germany and Britain issued a joint statement demanding that he force the separatists to "finally allow rescuers and investigators to have free and total access to the zone".
Rutte said the Dutch foreign minister was headed to the UN to lobby "to further expand the international coalition pushing for quick recovery of the bodies and getting to the bottom of the terrible events on MH17."
In the Netherlands, worshippers at church services prayed for the victims.
Silene Fredriksz-Hoogzand, whose son, Bryce, and his girlfriend, Daisy Oehlers, were among those killed, said she was appalled their bodies weren't being handed over.
"Mr Putin, send my children home," she said, speaking on Sky TV from Amsterdam's Schiphol Airport. "Send them home. Please."