A London court ruled on Monday that Julian Assange, the embattled WikiLeaks founder, could appeal his extradition to the United States, a move that opens a new chapter in his prolonged fight against the order in Britain’s courts.

Two High Court judges said they would allow an appeal to be heard on a limited number of issues.

In March, the judges said that the court would grant a request to appeal unless the American government gave “a satisfactory assurance” that Mr. Assange would be afforded protections under the U.S. Constitution, would not be “prejudiced by reason of his nationality,” and that “the death penalty is not imposed.”

The U.S. Embassy in Britain provided assurances on those issues in a letter sent in April, but Mr. Assange’s legal team had argued in court that they did not all go far enough to meet the court’s request.

Mr. Assange, 52, has been held in Belmarsh, one of Britain’s highest-security prisons, in southeastern London since 2019 as his fight against the extradition order has proceeded through the courts.

He faces charges in the United States under the Espionage Act related to WikiLeaks’ publication of tens of thousands of secret military and diplomatic documents leaked to the site by Chelsea Manning, an Army intelligence analyst, in 2010.

In June 2012, Mr. Assange entered the Ecuadorean Embassy in London, where he stayed for the next seven years over fears that he could be arrested. He was eventually evicted from the embassy in 2019 and was promptly arrested.

The U.S. Justice Department had charged Mr. Assange with 18 counts of violating the Espionage Act by participating in a criminal hacking conspiracy and by encouraging hackers to steal secret material. In 2021, the extradition order for Mr. Assange was denied by a British judge, who ruled that he would be at risk of suicide if sent to a U.S. prison, but the High Court later reversed that decision. In 2022, Priti Patel, Britain’s home secretary at the time, approved the extradition request.

An earlier request from Mr. Assange’s legal team for an appeal was rejected by a judge, before the two judges who made Monday’s decision decided that his appeal could go ahead.

Since his arrest in 2019, Mr. Assange has rarely been seen, and in his final hearing on Monday he decided not to attend the hearing for undisclosed health reasons, according to his legal team. Throughout his time in prison, his lawyers and his wife, Stella Assange, have warned about his diminishing physical and mental health. In 2021, Ms. Assange had a small stroke. Speaking ahead of the final hearing, Ms. Assange said her concerns for his mental health were “very serious.”

Kristinn Hrafnsson, editor in chief of WikiLeaks, said at a news briefing last week that Mr. Assange’s legal team had been focusing its efforts on a political resolution, which he said “has been bearing fruit.”

“More and more political leaders are coming to the side of Julian,” Mr. Hrafnsson said, “They see the absurdity in this case. And how serious the implications this would have for press freedom worldwide.”

The Australian government has put its support behind Mr. Assange, an Australian citizen, and Prime Minister Anthony Albanese has said he hopes the case can be “resolved amicably.”

Last month, President Biden said that the administration was considering a request from Australia that Mr. Assange be allowed to return there and not face prison, prompting speculation that Washington could be rethinking the case. The U.S. Department of Justice declined to comment at the time.

Supporters have long argued that Mr. Assange’s life could be at risk if he were sent to the United States for trial. While Mr. Assange’s lawyers say that he could face up to 175 years in prison if convicted, lawyers for the U.S. government have said that he would be more likely to be sentenced to four to six years.

In the court on Monday, Mr. Assange’s legal team said that the assurances offered by the U.S. side that it would not seek the death penalty were sufficient, but raised issues with the promise that if Mr. Assange were extradited, he would “have the ability to raise and seek” the rights and protections given under the First Amendment.”

“We say this is a blatantly inadequate assurance,” Edward Fitzgerald, one of Mr. Assange’s lawyers said, arguing that, “There is no guarantee that he will be even permitted to rely on the First Amendment.”

James Lewis, a lawyer for the U.S., reiterated throughout the hearing that assurances provided by their side did make it clear that Mr. Assange would have ample protections to abide by Britain’s extradition law.

The prolonged nature of Mr. Assange’s case is not unheard-of, in part because of Britain’s extradition rules, which allow for appeals on a variety of issues, said Nick Vamos, former head of extradition for the British Crown Prosecution Service.

“The courts will entertain lots of different kinds of arguments about fairness and prison conditions and human rights and political motivations and all of those things,” Mr. Vamos said, adding that, ultimately, this may have allowed Mr. Assange to “buy time” for a political solution.