Assange, 50, is wanted in the US over an alleged conspiracy to obtain and disclose national defence information following WikiLeaks’ publication of hundreds of thousands of leaked documents relating to the Afghanistan and Iraq wars.
In December last year, US authorities won their High Court challenge to overturn a judge’s earlier ruling that Assange should not be extradited due to a real and “oppressive” risk of suicide.
The WikiLeaks founder’s lawyers are seeking to appeal that decision at the Supreme Court, arguing it raises “serious and important” legal issues.
For a proposed appeal to be considered by the UK’s highest court, a case has to raise a point of law of “general public importance”.
On Monday, two senior judges ruled there was a point of law, but refused permission for the appeal.
However, Lord Chief Justice Lord Burnett, sitting with Lord Justice Holroyde, said Assange could go to the Supreme Court itself and ask to bring the appeal.
“Whether or not the issue needs ventilation in that court is a matter appropriately for its decision,” Lord Burnett said.
He also asked the Supreme Court to “take steps to expedite consideration” of any application for an appeal.
Assange’s lawyers now have 14 days to make the application to the Supreme Court.
Assange’s fiancee, Stella Moris, hailed Monday’s court pronouncement as a win, but said Assange was still “far from achieving justice in this case”.
Speaking outside the Royal Courts of Justice, she said: “But let’s not forget that every time we win, as long as this case isn’t dropped, as long as Julian isn’t freed, Julian continues to suffer.
“For almost three years he has been in Belmarsh prison and he is suffering profoundly, day after day, week after week, year after year. Julian has to be freed and we hope that this will soon end.”
She added: “Our fight goes on and we will fight this until Julian is free.”
In her January 2021 ruling blocking the extradition, then-district judge Vanessa Baraitser found in favour of the US on all issues except Assange’s mental health.
Assange has previously indicated that he wants to challenge the original judge’s other findings at a later date.
Overturning the block on the extradition in December, senior judges found that Judge Baraitser had based her decision on the risk of Assange being held in highly restrictive prison conditions if extradited.
However, the US authorities later gave assurances that Assange would not face those strictest measures either pre-trial or post-conviction unless he committed an act in the future that required them.
Lord Burnett previously said that if the original judge had been given those assurances at the time of her ruling, “she would have answered the relevant question differently”.
In Monday’s pronouncement, Lord Burnett said the point of law was about the circumstances in which an appeal court can be given assurances by a country that were not given at the original extradition.
He added that “although the law in this jurisdiction has long been settled it does not appear that the Supreme Court has considered the question.
“Assurances are at the heart of many extradition proceedings.”