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The prime minister says Australia will do everything in its power to ensure the bodies of 37 Australians killed in the disaster are respected and justice is done.
Continuing his tough talk over the tragedy on Sunday evening, Mr Abbott said he had attended a national security committee of cabinet meeting after images emerged of the crash site in eastern Ukraine being "absolutely trampled".
He said the discussion was dominated by concerns to ensure the bodies were treated with respect and taken to a place where a proper investigation could be carried out.
Earlier in the day he attended a memorial service in Sydney for the nearly 300 MH17 passengers killed. These were "wrenching times", he said, adding that his own daughters had recently travelled on the same flight from Europe.
Appearing on 60 Minutes on Sunday night, Mr Abbott said: "We owe it to the dead, all the dead, we owe it to the families, all the families to do everything in our power to respect the bodies, to find the truth and to ensure justice is done."
He said Foreign Minister Julie Bishop was in New York prosecuting Australia's case before the Security Council for an immediate securing of the crash site, proper treatment of the bodies and a full and fair investigation.
The domestic focus on the disaster has now shifted to Mr Putin's attendance at the Brisbane G20 meeting in November, with Labor and the Greens and Queensland Premier Campbell Newman all demanding Russian co-operation in the investigation before he is welcomed.
Ms Bishop will stay in New York "for as long as needs be", Mr Abbott said.
He said an investigation needed access to the debris, the black box and any person who can shed light on the crash.
"We are consulting with our friends, we are consulting with our allies because frankly it is simply unacceptable to see what is happening on this site given that 298 innocent people have been murdered," Mr Abbott said.
Mr Abbott said he was seeking a conversation with Mr Putin to call for Russia's assistance in repatriating the bodies from eastern Ukraine.
"If he wants to be a friend of Australia, if he wants to be a friend of decency and humanity all assistance that he might be able to offer would be deeply appreciated at this time," Mr Abbott told 60 Minutes.
Russia has agreed to an investigation, amid mounting scepticism about its willingness to co-operate with the international community.
Earlier, Mr Abbott said he held fears of continued interference at the site.
"My fear is that Russia will say the right thing, but that on the ground interference with the site, interference with investigators, interference with the dignified treatment of bodies will continue," he told ABC Television.
Following the national security committee of cabinet meeting Mr Abbott said if he was able to speak with the Russian president he would put the case for common decency but other options were being considered.
"We are looking at all the options, we are in discussion with our friends because what is happening at the moment is simply unacceptable, it is intolerable," Mr Abbott said.