The 50-year-old Australian is wanted in the United States to face trial on 18 charges including breaking an espionage law after WikiLeaks published thousands of secret US files and diplomatic cables in 2010.
The United States is appealing against a January 4 ruling by a British judge that Assange should not be extradited because his mental health was such that he would likely take his own life in a US prison.
Assange's lawyers told the Court of Appeal it should disregard assurances given by the United States as part of the appeal that he would not be subject to harsh detention conditions known as Special Administrative Measures (SAMs).
They said that regardless of whether he was technically subject to SAMs the evidence heard during the original extradition hearing showed he would be detained "in conditions of extreme isolation" that could drive him to suicide.
Lawyer Mark Summers also raised a report, published last month by Yahoo News, that alleged that in 2017 the CIA had considered killing or kidnapping Assange.
The CIA has declined to comment on the report and lawyers representing the United States did not address it during their submissions to the court on Wednesday.
Summers said that the report showed there was a risk the CIA could use its powers to certify that Assange should be subjected to SAMs "the moment he sets foot in the USA" and that the wording of the US assurances would allow that to happen.
Assange, who denies any wrongdoing, is being held at Belmarsh Prison in London and was not in court during the hearing.
A US lawyer said four "binding" diplomatic assurances had been made, including that it would consent to Assange being transferred to Australia to serve any prison sentence he may be given.
Lord Chief Justice Lord Burnett, sitting with Lord Justice Holroyde, said lawyers had given them "much to think about" and that they would "take time to consider our decision" at the end of legal arguments on Thursday.
WikiLeaks came to prominence in 2010 by publishing vast troves of confidential US records which the country's officials said put lives in danger.
Soon afterwards, Sweden sought Assange's extradition from the UK over allegations of sex crimes.
He was ordered to be sent to Sweden in 2012 but instead fled to the Ecuadorean embassy in London and lived there for seven years.
He was dragged out in April 2019 and jailed for breaching his British bail conditions although the Swedish case against him had been dropped.
The US authorities then sought his extradition.
Supporters see Assange as an anti-establishment hero victimised for exposing US wrongdoing in Afghanistan and Iraq.
Critics say he recklessly endangered the lives of agents named in the leaked material.
About 80 supporters staged a noisy rally outside the London court ahead of the hearing, playing music and chanting "Free Julian Assange".
with reporting by PA and AP
