Foreign Minister Julie Bishop says the government, including Prime Minister Tony Abbott, is making daily representations in a bid to save death row inmates Andrew Chan and Myuran Sukumaran.
Ms Bishop says she spoke with the men's families, who are in Bali, on Monday night.
"We're making representations, privately and publicly, to stay the execution," she told Nine Network on Tuesday.
"And we will not give up, we continue to do that on a daily basis.
"The prime minister has been making representations to the Indonesian president."
Ms Bishop said Australia will continue to ask for clemency for both men, who have made an "extraordinary advance" in their rehabilitation.
"The challenge, of course, is that drug trafficking is an offence in Indonesia that carries the death penalty in many instances," she said.
"It's a sovereign nation with its own judicial system."
President Joko Widodo will deny clemency to 64 drug offenders who have been sentenced to death, believing only executions can shock the republic out of a "drugs crisis".
The Australians are expected to be executed this month.
