LONDON — A British court ruled Tuesday that Julian Assange can’t be extradited to the United States on espionage charges unless American authorities guarantee he won’t get the death penalty, giving the WikiLeaks founder a partial victory in his long legal battle over the site’s publication of classified documents.

Two High Court judges said they would grant Mr. Assange a new appeal unless American authorities give further assurances within three weeks about what will happen to him.

The ruling means the legal saga, which has dragged on for more than a decade, will keep going while Mr. Assange is behind bars at London’s high-security Belmarsh Prison, where he has spent the last five years.

Judges Victoria Sharp and Jeremy Johnson said America must guarantee that Mr. Assange, who is Australian, “is afforded the same First Amendment protections as a United States citizen, and that the death penalty is not imposed.”

The judges said that if America files new assurances, “we will give the parties an opportunity to make further submissions before we make a final decision on the application for leave to appeal.” The judges said a hearing will be held May 20 if America makes those submissions.

Mr. Assange’s supporters say he is a journalist protected by the First Amendment who exposed American military wrongdoing in Iraq and Afghanistan that was in the public interest. They have argued his prosecution is politically motivated and he can’t get a fair trial in America.

Mr. Assange’s wife Stella Assange said the WikiLeaks founder “is being persecuted because he exposed the true cost of war in human lives.”

“The Biden administration should not issue assurances. They should drop this shameful case, which should never have been brought,” she said outside the High Court in London.

The ruling follows a two-day hearing in the High Court in February, where Mr. Assange’s lawyer Edward Fitzgerald said American authorities were seeking to punish him for WikiLeaks’ “exposure of criminality on the part of the U.S. government on an unprecedented scale,” including torture and killings.

The American government said Mr. Assange’s actions went beyond journalism by soliciting, stealing and indiscriminately publishing classified government documents that endangered innocent lives.

The judges rejected six of Mr. Assange’s nine grounds of appeal, including the allegation that his prosecution is political. They said that while Mr. Assange “acted out of political conviction … it does not follow however that the request for his extradition is made on account of his political views.”

They accepted three grounds or appeal: the threat to Mr. Assange’s freedom of speech, Mr. Assange’s claim that he faces disadvantage because he is not an American citizen, and the risk he could receive the death penalty.

American authorities have promised Mr. Assange would not receive capital punishment, but the judges said that “nothing in the existing assurance explicitly prevents the imposition of the death penalty.”

Mr. Assange, 52, an Australian computer expert, has been indicted in America on charges over Wikileaks’ publication in 2010 of hundreds of thousands of classified documents.

Prosecutors say he conspired with U.S. army intelligence analyst Chelsea Manning to hack into a Pentagon computer and release secret diplomatic cables and military files on the wars in Iraq and Afghanistan.

Mr. Assange faces 17 espionage counts and one charge of computer misuse. If convicted, his lawyers say he could receive a prison term of up to 175 years, though American authorities have said any sentence is likely to be much lower.

Mr. Assange’s wife and supporters say his physical and mental health have suffered during more than a decade of legal battles, including seven years in self-exile in the Ecuadorian Embassy in London and the last five years in prison.

Mr. Assange’s legal troubles began in 2010, when he was arrested in London at the request of Sweden, which wanted to question him about allegations of rape and sexual assault made by two women. In 2012, Mr. Assange jumped bail and sought refuge inside the Ecuadorian Embassy.

The relationship between Mr. Assange and his hosts eventually soured, and he was evicted from the embassy in April 2019. British police immediately arrested and imprisoned him for breaching bail in 2012. Sweden dropped the sex crimes investigations in November 2019 because so much time had elapsed.

A British district court judge rejected the American extradition request in 2021 on the grounds that Mr. Assange was likely to kill himself if held under harsh American prison conditions.

Higher courts overturned that decision after getting assurances from America about his treatment. The British government signed an extradition order in June 2022.

This article has been updated.