A London judge ruled in January that the Wikileaks foudner should not be extradited to the United States to face criminal charges including breaking a spying law, saying his mental health problems meant he would be at risk of suicide.
The US government has appealed a British judge's decision to block the extradition of WikiLeaks founder Julian Assange to face trial for publishing military secrets.
In a document outlining their arguments on Wednesday, presented to the Court of Appeal and circulated to media, the lawyers said the United States had provided Britain with "a package of assurances" addressing the District Judge's concerns.
These included that Assange would not be subject to a set of strict detention conditions known as Special Administrative Measures and would not be detained at a maximum security penitentiary in Florence, Colorado, known as ADX.
The US authorities had also assured Britain that they would consent to Assange serving any custodial sentence imposed by a US court in Australia, the document said.
Washington has asked the High Court to overturn District Judge Vanessa Baraitser's January ruling that Assange is a serious suicide threat if extradited across the Atlantic.
The United States has said it was "extremely disappointed" at Baraitser's decision, arguing the judge "didn't appreciate the weight" of expert evidence that said Assange was not at risk of suicide.
Its lawyers have argued Baraitser was "misled" in evidence from Assange's psychiatric expert Michael Kopelman, who they claim concealed things such as that his client had fathered children while holed up in the Ecuadorian embassy in London.
During a preliminary hearing in August, the High Court granted the US government's request to appeal against the ruling on five grounds.
Whatever the court's two senior judges decide, months if not years of further legal wrangling loom.
If the US appeal is successful, the case will be sent back to a lower court for a new decision. And whoever loses can also ask for permission for a further, final appeal to the UK's Supreme Court.
Indicted by US
Assange, 50, was arrested in Britain in 2019 for jumping bail after spending seven years inside the Ecuadorian embassy to avoid extradition to Sweden where he faced allegations of sexual assault. These were later dropped.
Despite his extradition being blocked, he has been denied bail pending the outcome of the US appeal, amid fears he would abscond.
Assange is wanted in Washington to face 18 charges relating to the 2010 release by WikiLeaks of 500,000 secret files detailing aspects of military campaigns in Afghanistan and Iraq.
He has been indicted for violating the US espionage act and for hacking, based on the alleged assistance he provided former military intelligence officer Chelsea Manning in obtaining the documents from secure military computer systems.
If convicted in the US, he faces a maximum sentence of 175 years in jail.