The appeal came after President Joko Widodo rejected a plea for clemency from 31-year-old Andrew Chan, the ringleader of a failed bid to smuggle more than eight kilograms of heroin to Australia in 2005.
Widodo had already turned down an appeal for clemency from Myuran Sukumaran, Chan's collaborator in the scheme, which included seven other people who are serving lengthy prison sentences.
"While Australia respects Indonesia's sovereignty, we are asking that Indonesia reconsider its decision to execute two Australian citizens," Australian Prime Minister Tony Abbott said in statement.
"Both men are reformed characters and both have helped to rehabilitate other prisoners. The prerogative of mercy should be extended to them."
For the last 10 years, the pair has fought a lengthy legal battle, first to avoid conviction against charges and later to reduce the severity of their sentences.
The Bali 9 were arrested in April 2005 after Indonesian police received a tip-off from Australian Federal Police. They caught four at the Denpasar airport with more than eight kilograms of heroin strapped to their bodies.
Another four -- including Sukumaran -- were arrested at a hotel in the village of Kuta. Chan was detained after a boarding a plane to Sydney -- he wasn't carrying any drugs but was named by others as the mastermind of the plot.
During their 10 years of imprisonment, supporters say Chan and Sukumaran have changed their ways and are now working within the prison to help other inmates.
Lawyers had hoped their rehabilitation would count in their favor, but their failed clemency bids have reinforced efforts to pursue other legal avenues.
Chan's lawyers are said to be seeking to reopen the case, a controversial move that faces legal resistance from Indonesia's Supreme Court, according to Indonesia law expert Tim Lindsey.
Currently, the Constitutional Court allows an unlimited number of applications to reopen a case -- the Supreme Court does not.
"There's a dispute between the two courts at the moment. There've been attempts to bring them together to work out a resolution. It hasn't been successful. So as it stands, the Constitutional Court says this application is acceptable and the Supreme Court says it's not," Lindsey told the ABC.
Death for drugs
Indonesia has long taken a tough line on drug smugglers and Widodo has made it clear he doesn't intend to introduce a policy of leniency.
Last week, six prisoners were killed by firing squad
, including five foreigners from Brazil, the Netherlands, Malawi, Nigeria and Vietnam.
Brazil's President Dilma Rousseff issued a statement saying the execution of one of her countrymen had "severely affected" relations with Indonesia.
Australia's Abbott says in the best interests of Chan and Sukumaran, the government will make no further public comments but its "support will continue."