Those pleading for clemency for 25-year-old Nguyen Tuong Van planned to hold a mass and prayer vigil in Sydney's St Mary's Catholic Cathedral on Wednesday night.
Nguyen is scheduled to be hanged on Friday after he was caught with 396g of heroin - enough for 26,000 doses, officials say - strapped to his back at Singapore's Changi Airport.
Father John Usher, the chancellor of the Sydney Archdiocese, said: "Two wrongs don't make a right. Taking a human life is not a way of solving a problem."
The powerful Australian Transport Workers Union, which represents airport refuellers and baggage handlers, is threatening to boycott Singapore Airlines if the execution is not cancelled.
"Two wrongs don't make a right. Taking a human life is not a way of solving a problem"
Father John Usher,
Sydney Archdiocese chancellor
A petition for clemency with more than 50,000 signatures was to be presented to the Singaporean High Commission on Wednesday in Canberra, where a 3000-candle night vigil was planned.
Australia's Greens party has called for a minute's silence at 9am Sydney time on Friday, (2200 GMT Thursday), the time when Nguyen is to be hanged in Singapore's Changi Prison.
Supporting death penalty
But while Australia outlawed the death penalty decades ago, opinion polls indicate that many people still support capital punishment.
A headline of a letter published in the Sydney Morning Herald on Tuesday read: "Friday is the time to remember heroin's victims."
G Ward wrote in the letter: "My heart goes out to Nguyen's parents ... But get real Australia. This man, like all drug dealers, was prepared to trade the lives and future of a thousand of our children for a few miserable dollars."
A cartoon in Sydney's Daily Telegraph on Wednesday depicted a heroin addict, on the street in front of scores of needles, saying "What a shame he's being executed".
"This man, like all drug dealers, was prepared to trade the lives and future of a thousand of our children for a few miserable dollars"
G Ward, in letter published in the Sydney Morning Herald
The Daily Telegraph said in an editorial on Wednesday that "the suggestion that the nation should observe a minute's silence is both morbid and offensive", while South Australian state premier Mike Rann said a minute's silence would be offensive to war veterans.
"People know what the laws are [in Singapore] and they take the risks, they choose to play a form of Russian roulette," Rann said.
Opinion polls have shown Australians do not support boycotts against Singapore to protest over Nguyen's execution or possible government court action to fight for his life.
Singapore practises "long-drop hanging", an execution method inherited from British colonial days.
Convicts drop several feet and die when the spinal cord snaps, instead of by asphyxiation as is the case with "short-drop hanging".