"We are making urgent representations to the Indonesian government through the usual diplomatic channels," Abbott said.
"We oppose the death penalty for Australians, we oppose it at home -- we oppose it abroad," he told Channel Nine.
Myuran Sukumaran, one of nine Australians arrested in 2005 for attempting to smuggle eight kilograms of heroin out of the resort island of Bali, this week learned he had lost a bid for presidential clemency, his final chance to avoid execution.
"But I do have to say that it is incumbent upon us to respect the systems that other countries have," Abbott told Channel Nine's Today show.
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"While I would absolutely deplore the carrying out of the death sentence we are an important partner of Indonesia, friendship with Indonesia is important for Australia, and I want that to continue."
The other seven members of the "Bali Nine" were given life sentences. One later had her sentenced reduced to 20 years.
Indonesia enforces tough punishments for narcotics offences, with strong public support for executing drug traffickers.
Executions in Indonesia are usually carried out by firing squad.