No date for the executions of Andrew Chan and Myuran Sukumaran has been released but an Indonesian official said governments with death row prisoners had been invited to a meeting with the foreign ministry on Monday.
Chan, 31, and Sukumaran, 33, are facing execution by firing squad as ring leaders of the so-called Bali Nine group trafficking heroin from Indonesia's island of Bali into Australia.
"Millions of Australians are feeling very, very upset about what may soon happen to two Australians in Indonesia," Abbott told reporters in Sydney.
Australian media reported that there are 360 Indonesians on death row around the world, including in Malaysia, Singapore, China, Saudi Arabia and Qatar, with 230 of these on drugs charges.
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Abbott, in an interview with The Daily Telegraph, also noted that Australia had stood by close neighbour Indonesia in times of need, particularly after the devastating 2004 Asian tsunami.
"We abhor the death penalty, we regard it as barbaric," he told the paper.
"We respect Indonesia's sovereignty but we would very much appreciate an act of magnanimity in this case," he added.
Foreign Minister Julie Bishop has warned Jakarta against underestimating the strength of public feeling for the pair, sentenced to death in 2006 for attempting to mastermind the trafficking of more than eight kilogrammes (17.6 pounds) of heroin out of Bali into Australia the previous year.
She said travellers could choose to boycott Indonesia, whose Bali island is an extremely popular holiday spot with Australians.
But both have lost their appeals for clemency to new President Joko Widodo -- whose government recently executed six convicted drug smugglers.
Widodo has been a vocal supporter of capital punishment and has vowed a tough approach to ending what he has called Indonesia's "drug emergency".