The security council is set to vote on the resolution in New York around 3am Tuesday (NZ time). One of the sticking points with Russia, which has a veto on the council, appears to be the use of the term "shooting down" of the aircraft.
But Mr Abbott has no doubt it was shot down in a "criminal act" and is seeking advice on whether it can be declared a terrorist act, which would open the way for compensation payments for victims.
If Russia used its veto it would go down "very badly" in the international community. "We will do our best to craft a resolution which no reasonable person could object to," the prime minister said.
The resolution should open the way for retrieval of the bodies, securing of the site and the "administration of justice".
In a second phone call with US President Barack Obama, the two leaders agreed that Russia had a responsibility to use its influence to compel the separatists to co-operate with international investigators in a prompt, full, unimpeded and transparent way.
The Ukraine has delegated leadership of the investigation to Dutch officials. Former defence chief Angus Houston will lead Australia's efforts on the ground to recover, identify and repatriate the dead.
To date, the Australian government has deployed 45 officials to assist, including 20 from the Department of Foreign Affairs and Trade, 20 Australian Federal Police Officers, two Australian Transport Safety Bureau investigators and three Defence officials.
Mr Abbott also has spoken with the Dutch, British, Malaysian, Ukraine, German, French and New Zealand leaders in a round of telephone calls during the past few days. The mood of world leaders had become "firmer and sterner" than it was on Friday, because of mounting evidence MH17 was shot down by pro-Russian rebels "quite possibly supplied by the backer", he said.
The situation at the crash site was still "shambolic" and urgent action was needed to secure the site for independent investigators.
"Having those people in control of the site is a little like leaving criminals in control of a crime scene," Mr Abbott said.
Foreign Minister Julie Bishop is at the UN to prosecute Australia's case.
- AAP