Andrew Chan and Myuran Sukumaran, members of an Australian group dubbed the "Bali Nine" who were arrested on the Indonesia island of the same name in 2005, have lost their final appeals for clemency.
"I've been told that my son will be taken out and shot at any time. I don't know what to do," mother Raji Sukumaran told the Australian Broadcasting Corporation.
"He's done something stupid, he made a mistake, he's apologised for that and he's rehabilitated. Now I've been told he could just be given 72 hours and he'll be taken out and shot."
Last weekend, Indonesia put to death five foreigners and one local woman convicted of drugs offences, unleashing a diplomatic storm as Brazil and the Netherlands condemned the execution of their citizens.
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Both Raji Sukumaran and Chan's brother Michael Chan said they had confidence that the Australian government would do everything it could to prevent the executions.
"I'm not giving up, and I know the Australian government will do everything it can to bring the boys home, or even to stop the execution," Sukumaran said.
"We need to save the boys. They deserve a second chance," he said.
Earlier Saturday a lawyer for the two Australians said a legal team was preparing a bid for a judicial review for the pair involving "very serious, meritorious legal options".
"This is not some kind of scramble to gain a few weeks of life, or something like that," Julian McMahon told the ABC.
McMahon said the men were holding up well, despite their appeals for presidential clemency being rejected.