At the High Court, lawyers for the US government and Wikileaks founder Mr Assange made preliminary arguments before Lord Justice Holroyde and Mrs Justice Farbey.
After a multi-week extradition hearing, District Judge Vanessa Baraitser ruled in January that Mr Assange should not be sent to the US, citing a real risk of suicide.
The US government was allowed a limited appeal against her decision on three grounds, but the latest ruling adds two further points which open significant elements of the psychiatric evidence to challenge.
From the early hours, supporters gathered outside the central London court to demand that Mr Assange be set free.
Arriving at the court, Mr Assange’s partner Stella Moris said: “The US is exploiting the inherently unfair extradition arrangements with this country in order to arbitrarily prolong his imprisonment — an innocent man accused of practising journalism.”
Former Labour leader Jeremy Corbyn was also present, and told protesters: “The United States seems to have a sort of obsession with people who uncover the truths about US military presence around the world.
“They should wind their necks in and let Julian Assange go.”
Mr Assange, who has been denied bail despite Judge Baraitser’s ruling, attended the hearing by videolink from Belmarsh prison.
He appeared more gaunt than at his last court appearance, with straggling white hair and new large-frame glasses.
The US wants to try the Australian for 18 alleged offences relating to leaks, including the Afghan and Iraqi war logs that were published in 2010.
Clair Dobbin QC, for the US government, told the court that Mr Assange had “hoodwinked” medical experts and Judge Baraitser at his previous hearing.
Ms Dobbin told the court there was a need for “anxious scrutiny” of Mr Assange’s reported mental health.
The barrister said that part of the US government’s appeal will focus on the requirement in law that an individual must be “so ill” that they are unable to resist suicide for a decision to be taken not to prosecute – or in Mr Assange’s case, extradite – them.
“It really requires a mental illness of a type that the ability to resist suicide has been lost,” she said.
“Part of the appeal will be that Mr Assange did not have a mental illness that came close to being of that nature and degree.”
Ms Dobbin also accused key expert witnesses at last September’s extradition hearings of misleading the court.
Her fire was directed at Professor Michael Kopelman, head of the neuropsychiatry department at King’s College London, who provided the extradition hearing with two written reports and gave evidence in person over several hours in September.
His reports describe in great detail Mr Assange’s psychological and familial history, but the first of them did not mention that the Wikileaks founder had a partner and two small children — facts it has since transpired Prof Kopelman knew at the time.
He has since explained that he left out these details for fear that putting them in the public domain would create needless risk, particularly as Mr Assange had been threatened with kidnap and poisoning.
Edward Fitzgerald QC, for Mr Assange, told the court that Judge Baraitser had been made aware of the omission and the reasons for it and had accepted that it in no way affected the report, concluding that it was “impartial and dispassionate.”
But Lord Justice Holroyde ruled that reconsideration of this evidence was appropriate in the circumstances. He set the full appeal hearing for October 27 and 28.
It means that Mr Assange must now wait nearly three months to learn his fate, while remaining in Belmarsh prison.
He could apply for bail before that date, but previous applications have been denied.