Updated

The bodies of nearly 300 passengers and crew aboard the Malaysia Airlines jet shot down over Ukraine are being turned over to Dutch authorities, while the black boxes from Flight 17 were handed over to Malaysian authorities, pro-Russian separatists said Monday.

The announcement came amid increasing criticism of the separatists' handling of the crash site in eastern Ukraine, and charges that Moscow was helping ethnic Russian insurgents orchestrate a cover-up.

Malaysian Prime Minister Najib Razak told reporters Monday the leader of the pro-Russian rebels agreed to hand over both of the jetliner’s black boxes to Malaysian investigators in Ukraine.

Najib also said that the remains of 282 of the crash victims currently in the rebel-held eastern town of Torez are being moved by train to Kharkiv in Ukraine, where they will be handed over to Dutch authorities. The remains are then expected to be flown to Amsterdam.

Najib also said that as part of an agreement he reached with rebel leader Alexander Borodai Monday night, independent international investigators will be given "safe access" to the crash site.

More On This...

    Earlier Monday, international leaders said the probe into the downing of the Boeing 777 had turned “shambolic,” and an intercepted communication appeared to capture Moscow directing Russian separatists in Ukraine to keep evidence out of the hands of objective investigators.

    Since the plane went down over Ukraine near the Russian border on Thursday, killing all 298 aboard, separatists had kept investigators from the scene, seized the black boxes and even taken custody of corpses, packing them in body bags and onto refrigerated train cars. There were even reports of looting from the bodies, and the credit cards of the dead used by ghoulish thieves.

    Dutch Prime Minister Mark Rutte, whose country lost 192 citizens on the plane, told a news conference Sunday that repatriating the bodies was his "No. 1 priority." His persistence appears to have paid off as a refrigerated train bearing many of the bodies pulled away Monday from Torez -- 9 miles from the crash site.

    Earlier in the day, Dutch experts had called for a full forensic sweep of the Flight 17 crash site and told armed separatists guarding the rail cars that the train must be allowed to leave as soon as possible. AP journalists said the smell of decay was overwhelming at the Torez train station and many of the inspectors wore masks or pressed cloths to their faces on the sunny, hot day.

    A Ukrainian train engineer told The Associated Press that a power outage had hit the cars' refrigeration system for several hours overnight but was back up early Monday.

    Peter Van Vilet, leader of the Dutch National Forensic Investigations Team visiting Ukraine, said seeing the crash site in the farm fields near the eastern village of Hrabove was an emotional experience that gave him goose bumps despite the heat.

    “As anyone who has been watching the footage will know, this is still an absolutely shambolic situation,” Australian Prime Minister Tony Abbott said at a news conference. “The site is being treated more like a garden clean-up than a forensic investigation.”

    [pullquote]

    International outrage followed Ukraine’s SBU security agency’s release of audio recordings that appeared to capture separatists scheming with Moscow to seize the “black boxes,” or flight data recorders, from the wreckage.

    “I have a request for you. It is not my request,” a man identified as Battalion Vostok Commander Alexander Khodakovsky, a separatist leader, is heard saying on one recording. “Our friends from high above are very much interested in the fate of the black boxes. I mean people from Moscow.”

    Abbott on Monday likened leaving pro-Russian rebels in charge of the crash zone to “a little like leaving criminals in control of a crime scene.”

    Although several nations lost citizens aboard the flight, it is not clear who can or will conduct the full-scale investigation. The 9-mile debris field-- crucial to determining what happened to the plane -- lies within Ukraine but in territory controlled by ethnic Russian separatists. In addition to barring access to the site, there are reports that local residents have stolen from the dead.

    "The facts of looting, how the terrorists are dealing with the bodies, are beyond the moral boundaries," Ukrainian President Petro Poroshenko tweeted

    Dutch banks said Saturday they were taking "preventative measures" after reports of credit cards being looted from the crash site of Malaysia Airlines flight MH17.

    "International media report that victims' bank cards have been stolen," the Dutch Banking Association said in a statement. "Banks are taking preventative measures as necessary."

    French President François Hollande, after conferring with U.K. and German leaders, demanded that Putin force separatists in Eastern Ukraine to provide "free and total" access to the crash site. "If Russia does not immediately take the necessary measures, consequences will be decided by the European Union when its foreign-affairs council meets on Tuesday," Hollande's office said.

    Australian Foreign Minister Julie Bishop said it was “an utter outrage” that the site had been contaminated and evidence removed. “This is not a time to use bodies as hostages or pawns in a Ukrainian-Russian conflict,” Bishop told reporters in Washington.

    In Donetsk, separatist leader Alexander Borodai said “technical items” had been recovered.

    “Some items, presumably the black boxes, were found, and they have been delivered to Donetsk, and they are under our control,” he said at a news conference, adding that they were to be handed over to international experts.

    A senior National Transportation Safety Board source told Fox News the recovery of the black boxes was important, but investigators anticipate the boxes may only confirm that a missile brought down the flight, and not a mechanical failure. The data would not show who fired the missile and its origin.

    The type of missile could be determined with access to an uncontaminated crash site, the source said. Missiles leave explosive residue on the fuselage, which could help investigators identify the type of missile fired, and even its manufacturer.

    Moscow denies any involvement in the downing of the plane, by a Russian-made Buk surface-to-air-missile, from an area inside Ukraine controlled by Russian separatists. Russian President Vladimir Putin has blamed the incident on Ukraine, saying it occurred because Kiev has stoked the violent tensions between the Ukrainian government and ethnic Russians.

    "We can say with confidence that if fighting in eastern Ukraine had not been renewed on June 28, this tragedy would not have happened," Putin said. "Nobody should or does have a right to use this tragedy for such mercenary objectives."

    U.S. officials suspect that Russia supplied the rebels with several Buk, or SA-11 antiaircraft systems, by smuggling them into eastern Ukraine with other military equipment, including tanks. Those systems are believed to have been moved back into Russia following the downing of the jetliner.

    A team of international experts arrived in Kharkiv Monday, including 23 Dutch, three Australians, two Germans, two Americans, and one person from the U.K.

    Meanwhile, fighting flared again Monday between the separatists and government troops near the airport in the eastern rebel-held city of Donetsk, 30 miles west of the crash site. There were reports of several explosions and smoke rising from the area. Fighting began in mid-April between the government and the Russian-speaking separatists in eastern Ukraine after Russia annexed Ukraine's Crimean Peninsula a month earlier.

    The Associated Press contributed to this report.