Assange, who is Australian, on Wednesday lost a bitter legal battle to block his being sent from Britain to Sweden to face questioning over allegations of rape and sexual assault.
Two judges at the High Court in London rejected arguments by the 40-year-old, whose anti-secrecy website has enraged governments around the world, that his extradition would be unlawful.
Assange, a former computer hacker, now has 14 days to take the case to the Supreme Court, the highest legal authority in Britain.
His legal counsel Geoffrey Robertson called on the Australian government to step in. "I think Canberra may have to do something about it," he told the Australian Broadcasting Corporation.
"It's got a duty to help Australians in peril in foreign courts. It didn't do anything for David Hicks and that was something of a disgrace," he added, referring to the Australian formerly detained at Guantanamo Bay.
"As far as Julian Assange is concerned, Sweden doesn't have bail, doesn't have money bail for foreigners, so he's likely to be held in custody."
Robertson added that he does not believe the WikiLeaks founder, who has previously blasted Canberra for not doing enough to protect him amid the fallout from the leaks, will face a fair trial in Sweden.
"He's going to be tried in secret, and this is outrageous by our standards and by any standards," he said.
Assange has strongly denied the rape allegations, claiming they are politically motivated and linked to the activities of WikiLeaks. He has been under virtual house arrest since he was first detained in December.
He has expressed fears that his extradition to Sweden would lead to his transfer to the United States to face charges of spying linked to the leaking of classified military documents by US soldier Bradley Manning.
"We are, I think, most concerned to put at rest his danger of going to America and facing charges under the Espionage Act that could take years in prison," said Robertson, a renowned human rights campaigner.
Assange's mother told Australian media she believes her son would go to Sweden voluntarily to fight the charges provided the Australian government brokered a deal to ensure he will not be extradited to the US.
Christine Assange said Canberra should follow its own diplomatic and legal advice that her son was in "clear and present danger" and seek written guarantees he would not be sent on to the US.
"If that was to take place I believe Julian would go to Sweden and not resist it. His concern is that he'll be rendered on," she said.
She added that her son had been "crucified for doing what he was brought up to do".
"I brought my son up to tell the truth, to believe in justice. He was brought up to believe he lived in a democracy and to right any wrongs that he saw... Now I believe that's not true."
A spokesman for Foreign Minister Kevin Rudd told AFP the government would continue to provide Assange with full consular support.
He added: "The government has made it clear to the UK and Swedish government our expectation of due process, but Australia cannot directly intervene in legal processes of other countries."