The two leaders held a telephone conversation "to exchange their views on aspects of organising an independent and objective international inquiry", the Kremlin said in a statement.
They also stressed the need for compliance with a UN Security Council resolution calling for full access to the crash site and cooperation by all countries with the investigation.
Flight MH17 was shot out of the sky above east Ukraine on July 17 as it was heading from the Netherlands to Malaysia. Blame is largely falling on pro-Russian rebels fighting Ukrainian forces in the area who are restricting access to the crash site.
Abbott has accused the rebels of attempting a cover-up at the crash site to hide evidence. He has urged the world to press Moscow to help uncover the details of the downing of the plane, saying Russia could not "wash its hands" of the incident.