Nguyen is due to be executed on December 2, despite repeated protests by the Australian Government.
Secretary-General of the Singapore Democratic Party, Dr Chee Soon Juan, says Australia should appeal to other countries, including the United States, to put pressure on Singapore not to carry out its plan to hang Nguyen.
"I think Australia needs to approach the international community on this matter," he told ABC TV.
"It's just not a situation between Singapore and Australia, really it runs deeper and far wider than this.
"In the upcoming months and years you'll see a lot more people from around the world getting hanged for small time drug peddling in Singapore.
"I think every channel that is available right now ... every avenue that we can pursue, no stone must be left unturned and every country, every government that will listen to this call for justice and to put a stop to this insanity must be approached."
Nguyen was arrested in Singapore's Changi Airport in December 2002 while trying to board a flight to Australia with 396 grams of heroin strapped to his body and in his hand luggage.
He told police he had agreed to traffic drugs from Cambodia to Australia for a Sydney-based syndicate to help repay more than $30,000 in legal and other debts owed by his twin brother, Khoa.
Nguyen's lawyers have urged the Australian Government to take the case to the International Court of Justice (ICJ) to stop his execution, but several senior ministers have downplayed the chances of success.
Dr Chee said he believed Australia should take Nguyen's case to the ICJ as soon as possible.
"If the Singapore government wants to play at the international level then I think it's got to have a rethink of some of these very obsolete, these very archaic laws that serve no good for anybody," he said.
"I believe in the longer term the Singapore government can be made to see that this kind of a policy, this kind of law, does not serve its interests, does not serve the interests of the wider international community."