"I don't want to peddle false hope but I do want everyone to understand... We are straining every fibre to help these people in a difficult position," Abbott told reporters.
Andrew Chan and Myuran Sukumaran, on death row since 2006, face execution by firing squad as ring leaders of the so-called Bali Nine group trafficking heroin from Indonesia's Bali island into Australia.
The pair recently lost their final appeals to Indonesian President Joko Widodo for clemency despite arguing that they had rehabilitated themselves in prison.
The Sydney Morning Herald reported that the six judges who handed down the death penalties in 2006 were accused by the pair's lawyers of offering lighter sentences in exchange for money.
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The allegation is contained in a letter from the lawyers to Indonesia's judicial committee claiming a breach of ethics, the newspaper said.
The lawyers, led by Todung Mulya Lubis, added that the judges came under pressure from "certain parties" to deliver death sentences, the daily said.
"We certainly appreciate that the Indonesian government doesn't normally go ahead with executions of this type while there are legal options still available.
"We will be trying to ensure that all legal options are exhausted before something dreadful, final and irrevocable takes place."
Foreign Minister Julie Bishop warned last week that Australian tourists could boycott Indonesia if Chan, 31, and 33-year-old Sukumaran are executed.
Widodo has been a vocal supporter of capital punishment and pledged a tough approach to end what he has called the nation's "drug emergency".