Abbott held a tense 15-minute conversation with Russian President Vladimir Putin on the sidelines of the Asia-Pacific Economic Cooperation (APEC) meetings in Beijing, with the Kremlin revealing "the catastrophe of the Malaysian airliner was the main topic of conversation", Xinhua reported.
The MH17 disaster occurred in eastern Ukraine in July, killing all 298 passengers and crew members on board, including 38 Australians. Both Kiev and the West have since claimed that Russian missiles were responsible for bringing the aircraft to ground.
Abbott had previously accused Russia of supplying equipment, including weapons, to separatists in eastern Ukraine. However, Russia has continued to reiterate that Ukraine must take full responsibility for the attacks.
Last month, Abbott had famously vowed to "shirtfront" Putin when he next met with the Russian leader. Despite not following through on his promise, the Australian prime minister confirmed he held robust conversations with Putin.
Abbott is also said to have drawn comparisons between MH17 and Iran Air Flight 655.
In 1988, the US accidentally shot down an Iranian plane carrying 290 civilians. Abbott suggested the precedence set by then-President Ronald Reagan in compensating and apologising to families of the victims should be followed by Russia.
"The prime minister observed that when the US had inadvertently shot down a civilian aircraft, it had duly apologised and made appropriate restitution," the statement continued.
Both Abbott and Putin are said to have then agreed that the aforementioned information should be provided to the independent investigation.
The Kremlin also reiterated that Russia was keen to ensure the investigation remained unbiased and brought forward all relevant information in relation to how the aircraft was brought to ground.