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“Now they have to wait for another few months. We are hardened by now, but of course this is still stressful,” he said.

Mr. Assange was accused of rape, coercion and molestation following encounters with two Swedish women in August 2010. Swedish authorities issued a European arrest warrant on rape and molestation accusations, and Mr. Assange was arrested in London in December.

He was released on bail on condition that he live — under curfew and electronically tagged — at a supporter’s country estate in eastern England.

In February, Judge Howard Riddle ruled that Mr. Assange can be extradited to Sweden to face questions about the allegations, rejecting claims by him that he would not face a fair trial there.

Mr. Assange appealed, and he and his lawyer appeared at the High Court on July 12 to argue that the sexual encounters were entirely consensual and legal in the context of English law.

Two High Court judges rejected the 40-year-old hacker’s challenge, and Mr. Assange challenged the judges’ decision, filing papers to ask for his case to be taken to the Supreme Court.

Some of Mr. Assange’s supporters gathered outside the court before the hearing began. One banner draped over railings outside the court read: “Free Assange. Free Manning,” referring to U.S. Army analyst Bradley Manning, who is in custody at Fort Leavenworth prison in Kansas, suspected of disclosing secret intelligence to WikiLeaks.

Associated Press writer Malin Rising in Stockholm contributed to this report.