"It's a most unfortunate, barbaric act that is occurring," Attorney-General Philip Ruddock told Australia's Sky television on Thursday.
Nguyen Tuong Van, a 25-year-old former South Vietnamese refugee, is scheduled to die at dawn on Friday with all legal avenues for saving his life apparently exhausted.
As the Australian government urged Singapore to allow Nguyen's mother a final farewell hug with her son before he goes to the gallows, a poll showed that Australians were divided over whether he should die.
A Roy Morgan poll published on Thursday showed that 47% of people believed the death sentence should be carried out compared to 46% who said it should not.
The telephone poll of 654 people did not give a margin of error.
Nguyen was convicted of smuggling 400 grams (0.9 lb) of heroin from Cambodia through Singapore's Changi airport in 2002.
"It's a most unfortunate, barbaric act that is occurring"
Commenting on the case Ruddock criticised the imposition of the death penalty, especially in Nguyen's case which he said had mitigating circumstances.
Nguyen said he smuggled the drugs to try and pay off loan-shark debt for his brother in Australia.
"It was a mandatory death sentence. We feel most remorseful this is going to happen," Ruddock told Australian television.
On Wednesday, hundreds of people held a candlelit vigil outside Australia's Parliament House in Canberra to show support for Nguyen.
More supporters planned to rally in downtown Sydney on Friday morning at the appointed time of Nguyen's execution.
Australia scrapped the death penalty in 1973 and hanged its last criminal in 1967, while Singapore has executed more than 100 people for drug-related offenses between 1999 and 2003.
Singapore rejected five personal pleas for clemency for Nguyen from Prime Minister John Howard, who lobbied the city-state along with other ministers.
Protesters say the death penalty
does not prevent drug trafficking
However, Singapore bowed on Thursday to Australian pressure to allow Nguyen to touch his mother and twin brother during their final visit.
"Mr. Nguyen will be allowed to hold hands with his mother and brother," a statement released by the High Commission in Canberra said.
Under Singaporean law, all phsysical contact between condemned prisoners and relatives is usually banned.
Nguyen's mother Kim and twin brother, Nguyen Khoa, entered the jail early on Thursday afternoon. A friend, Kelly Ng, also visited.
"We've just had a beautiful last visit. It was a great visit and quite uplifting," said Lex Lasry, one of Nguyen's lawyers.
He brushed away tears as he spoke to the media.
Foreign Minister Alexander Downer had pleaded with Singapore officials that the 25-year-old's mother be allowed to give him a hug.
"It's just my view that they should have some contact before he dies," Downer told reporters.
Singapore previously had rejected requests from family and loved ones to have any physical contact with condemned prisoners.
Death row inmates at Changi Prison are separated from their visitors by a pane of glass.
On Thursday, Singapore's High Commissioner to Australia Joseph Koh gave a rare media interview on the case, but did not directly answer when asked whether he thought that refusing clemency would damage relations between the two countries.
"I think the bigger picture is that Singapore highly values good relations with Australia and with Australian leaders," Koh said. "We share a common belief in the sanctity of the law."
"It is for this reason that the Singapore Cabinet actually deliberated at length on the clemency petition," he added.
Some 420 people have been hanged in Singapore since 1991, mostly for drug trafficking, an Amnesty International 2004 report said.
That gives the country of 4.4 million people the highest execution rate in the world relative to its population.