* PM Abbott spoke with Russia's Putin overnight
* Putin needs to back words with actions -Abbott
* 45-strong Australian investigation team heading to Ukraine
* Western leaders "firmer, sterner" now, says Abbott (Adds Russian support for U.N. measure)
By Lincoln Feast
SYDNEY, July 21 (Reuters) - Australia's prime minister voiced deep concern on Monday that Russian-backed rebels remained in control of the crash site of a Malaysian airliner shot down over Ukraine, saying the site looked more like a "garden clean-up" than a forensic investigation.
At least 27 Australian passengers were among the 298 people aboard Malaysian Airlines Flight MH17, shot down over eastern Ukraine in an attack the West has blamed on separatist rebels armed by Russia.
Prime Minister Tony Abbott, speaking on a breakfast radio show, said he had spoken "overnight" to Russian President Vladimir Putin for the first time about the disaster, amid mounting horror over the treatment of victims' remains.
"He said all the right things and now we need him to be as good as his word," Abbott told 2GB radio, declining to comment in detail about his discussion with Putin.
U.S. Secretary of State John Kerry on Sunday demanded Moscow take responsibility for the actions of pro-Russian rebels whom Washington suspects of downing the jet with a missile. He expressed disgust at their "grotesque" mishandling of the bodies.
Moscow denies any involvement in the disaster and has blamed the Ukrainian military.
Television images of the rebel-controlled crash scene, where the remains of victims had lain decomposing in fields among their personal belongings, have turned initial shock and sorrow after Thursday's disaster into anger. The bodies had been removed from much of the crash site by Sunday, with many placed in refrigerated train wagons.
"Given the almost certain culpability of the Russian-backed rebels in the downing of the aircraft, having those people in control of the site is a little like leaving criminals in control of a crime scene," Abbott later told reporters.
AUSTRALIA PUSHES FOR UN RESOLUTION
A 45-strong Australian investigation team was either in or heading to Kiev, but had so far been unable to travel to the site despite some improvement in access.
"There's still a hell of a long way to go before anyone could be satisfied with the way that site is being treated," Abbott said. "It's more like a garden clean-up than a forensic investigation. This is completely unacceptable."
Heading the Australian group is retired Navy officer Angus Houston, who had been leading the search for Malaysian Airlines Flight MH370 which disappeared in March and is believed to have crashed off the west Australian coast. A C17 military transport aircraft is also on standby to fly to Ukraine.
Abbott, who has been the most outspoken leader regarding Russia's role in the disaster, said he had spoken to many Western leaders in the past two days and had noted "a much firmer and sterner mood" now.
Australia is leading a push for a binding U.N. resolution that demands those responsible be held accountable and that armed groups do not compromise the crash site integrity.
Russia's ambassador to Australia told the Australian Financial Review on Monday that it would support the resolution, provided it did not point fingers at Moscow or its proxies.
"This resolution is supported by Russia ... so long as it does not blame somebody," Morozov said in an interview, the newspaper reported.
Abbott said that any effort by Russia to block or delay a resolution would be viewed "very, very badly" by Australia.
Abbott is due to host Putin and other world leaders at the G20 Leaders Summit in November and is facing mounting calls to ban the Russian leader from participating.
"There's a lot of water that will almost certainly flow under the bridge between now and November and I just think it's unhelpful to start speculating about what might happen in four months now," he said. (Additional reporting by Jane Wardell and Matt Siegel; Editing by Mark Bendeich and Clarence Fernandez)