WikiLeaks founder Julian Assange arrives at court in London, May 1, 2019, to be sentenced for bail violation. He was sentenced to 50 weeks in prison. Getty

London -- WikiLeaks founder Julian Assange faced a court hearing Thursday over the U.S. request to extradite him for allegedly conspiring to hack a Pentagon computer. Assange appeared by video link from prison for the hearing at London's Westminster Magistrates' Court.

According to a reporter for The Guardian newspaper who was in the courtroom, the judge asked Assange whether he would voluntarily surrender to the U.S. extradition request.

"I do not wish to surrender myself for extradition for doing journalism that has won many, many awards and protected many people," Assange replied. The judge adjourned the brief proceeding and said the next hearing, another procedural one, would be held on May 30, with a more substantial hearing set for June 12, according to the Reuters news agency.

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A few dozen supporters holding signs reading "Free Assange" and "No extradition" gathered outside the courthouse before the hearing. It's an early stage in what is likely to be a months- or years-long extradition process.

The 47-year-old Australian was sentenced Wednesday to 50 weeks in prison for separate charges on jumping bail in 2012 and holing up in the Ecuadorian Embassy in London. At the time, he was facing extradition to Sweden for questioning over rape and sexual assault allegations made by two women.

Assange said he took to hiding in the embassy out of fear -- what he called "terrifying circumstances" -- of being sent to the U.S. to face charges related to WikiLeaks' publication of classified U.S. military documents.

WikiLeaks editor-in-chief Kristinn Hrafnsson said Wednesday that the extradition battle was "a question of life and death" for Assange.

Assange was arrested last month after his relationship with his embassy hosts went sour and Ecuador revoked his political asylum.

What is the U.S. case about?

Lawyers have said Assange will fight extradition to the U.S., where authorities have charged him with conspiring to break into a Pentagon computer system.

The Justice Department's indictment shows that Assange has been charged with computer hacking crimes for trying to illegally access "secret" materials on a U.S. government computer. The charge is officially listed as "conspiracy to commit computer intrusion."

The indictment accuses Assange of trying to access the secret material "with reason to believe that such information so obtained could be used to the injury of the United States and the advantage of any foreign nation."

The charges relate to materials stolen by former Army intelligence analyst Chelsea Manning, who was convicted in 2013 of leaking classified government and military documents to WikiLeaks. She had worked as an intelligence analyst in Iraq and was arrested in 2010. Manning is transgender and at the time of her arrest, her name was Bradley.

Manning was jailed again in March for refusing to testify to a grand jury investigating WikiLeaks. U.S. District Judge Claude Hilton ordered Manning to jail for contempt of court after a brief hearing in which Manning confirmed she had no intention of testifying.

Duelling extradition bids?

The case against Assange in Sweden was dropped by prosecutors in May 2017 -- not because of any conclusion about his guilt or innocence, but because they accepted there wasn't any reasonable chance of prosecuting him as he remained holed-up in London.

Swedish lawyer Elisabeth Massi Fritz, who represents one of the claimants behind the sexual abuse allegations, said shortly after Assange's arrest that it had "understandably come as a shock to my client that what we have been waiting and hoping for since 2012 has now finally happened."

Massi Fritz said in a tweet that she and her team would "do everything we possibly can to get the Swedish police investigation re-opened so that Assange can be extradited to Sweden and prosecuted for rape. No rape victim should have to wait 9 years to see justice be served."

Her client has claimed Assange had sex with her without a condom while she was asleep. In Sweden, having sex with an unconscious, drunk or sleeping person can lead to a rape conviction punishable by up to six years in prison.

Swedish law experts and Assange's own lawyer in Sweden have said, however, that it appears unlikely a new extradition request will be issued by the Scandinavian nation, simply due to the amount of time that has passed.

"I think it would be a very uphill task to reopen the investigation in Sweden," Britain's Guardian quoted former prosecutor Sven-Erik Alhemas telling a Swedish news agency. "Testimony usually weakens with time, and it's now been 10 years."

What happens next

If Swedish prosecutors do decide to reopen their investigation and issue a new arrest warrant for Assange, it will be down to U.K. Home Secretary Sajid Javid to make the decision on which request to honor -- if any.

More than 70 British legislators have urged Javid to give priority to a case involving rape allegations ahead of the U.S. request, if Sweden reopens the case.

A U.S. official told CBS News justice correspondent Paula Reid that even with an official U.S. request now filed with Britain, extradition is a lengthy process and the WikiLeaks boss was likely hit U.S. soil quickly.

That said, Britain and the U.S. do have a fast-track extradition agreement, so the process should be easier than it would be with many other nations.

Assange would not be expected to enter a plea to the Department of Justice charge unless he loses his extradition case in the U.K. and is brought to a courtroom in the United States.