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The 50-year-old Australian is wanted in the US on 18 criminal charges, including breaking a spying law, after his group published thousands of secret classified files and diplomatic cables in 2010.
The US is appealing against a decision by a British judge that Assange should not be extradited because he would be at high risk of committing suicide in an American prison.
"The United States has also provided an assurance that the United States will consent to Mr Assange being transferred to Australia to serve any custodial sentence imposed on him," said a document presented to the Court of Appeal in London by lawyers acting for the US government on Wednesday.
Lawyers for the United States argue that concerns around Assange's mental health should not prevent him from facing US justice.
Supporters of Assange gathered outside London's High Court from early on Wednesday, chanting "free Julian Assange", before his father and Stella Moris, his partner and mother of his two children, arrived.
Assange, who denies any wrongdoing, is being held at Belmarsh Prison.
The hearing is the latest stage in a legal battle that has been raging since 2012.
WikiLeaks came to prominence when it began to publish vast troves of confidential US military records and diplomatic cables which the US says put lives in danger.
Soon afterwards Sweden sought Assange's extradition from Britain over allegations of sex crimes. When he lost a case against extradition in 2012, he fled to the Ecuadorean embassy in London and stayed there before being finally dragged out in April 2019.
Assange was then jailed for breaching British bail conditions, although the Swedish case against him had been dropped, and the US authorities sought his extradition.
On January 4, a British judge rejected his argument that the case was political and an assault on freedom of speech, but said he should not be extradited because his mental health problems meant he would be at risk of suicide in a US prison.
Supporters see Assange as an anti-establishment hero who has been victimised because he exposed US wrongdoing in Afghanistan and Iraq and say his prosecution is a politically motivated assault on journalism and free speech.
US prosecutors and Western security officials regard him as a reckless enemy of the state whose actions threatened the lives of agents named in the leaked material.