Mr Abbott, who was prime minister at the time of the crash, dismissed the Russian claim that the deadly missile downing MH17 was fired outside territory held by Russian-backed militants, news.com.au reports.
"Russians would say that," he told 3AW on Tuesday.
The evidence showed a Russian missile battery crossing the border into the Ukraine, downing the jet and heading back to Russia, he said.
Mr Abbott doesn't lay personal blame solely with Russian President Vladimir Putin but says the leader bears a heavy responsibility.
Read alsoMH17 crash in Donbas: Bellingcat explains why Russia provides radar data so late"I think the sooner Russia owns up to its role in all of this, and does what it can to offer restitution to the families of the victims, the better."
The Russian military claim comes two days before a Dutch-led investigative team is to release a report on where the missile was fired.
A Dutch Safety Board investigation reported last year a missile was fired from rebel-held territory, but did not specify who had fired it.
Russia has consistently rejected allegations that rebels fired the missile.