The Labour leader urged the UK government to oppose the attempt to put the 47 year-old WikiLeaks founder to trial for obtaining classified information from former US Army intelligence analyst Chelsea Manning.
Assange faces a maximum five year sentence if convicted of “conspiracy to commit computer intrusion” but officials are said to be considering bringing further charges.
Nearly 12 hours after Assange’s arrest on Thursday morning, Mr Corbyn tweeted: “The extradition of Julian Assange to the US for exposing evidence of atrocities in Iraq and Afghanistan should be opposed by the British government.”
His statement accompanied a video posted by shadow home secretary Diane Abbott, who referred to the WikiLeaks founder as a whistleblower who was “being pursued because he has exposed wrongdoing by US administrations and their military forces.”
Ms Abbott said Mr Assange’s extradition could be prevented on “human rights grounds” and cited the case of British hacker Gary McKinnon, whose deportation to the United States was blocked by Theresa May in 2012.
In a radio interview, she was asked repeatedly about allegations of rape made against Mr Assange in Sweden, replying: “Those charges were never brought.”
Prosecutors in Stockholm dropped the rape investigation in 2017 because they “could not advance” while Assange remained in the embassy, but are now considering reopening it.
Ms Abbott told BBC Radio 4’s Today programme: “We all know what this is about. It’s not the rape charges, serious as they are, it’s about Wikileaks.
“All that embarrassing information about the activities of the American military that was made public and that is what it is about.”
She added: “If the Swedish government wants to come forward with those charges, I believe that Assange should face the criminal justice system.
“But if you’re talking about the American extradition attempt – which is less about the threat he poses to security in American and more about the embarrassment about the things he has revealed about the American military and security services – but we would say just as in the end we blocked the extradition of Gary McKinnon, we should block the extradition of Assange.”
Theresa May and several cabinet ministers including home secretary Sajid Javid welcomed the arrest.
Assange spent seven years at the Ecuadorian embassy in London before being detained on a US extradition warrant and for breaching bail.
He was convicted of the bail offence on Thursday afternoon after appearing at Westminster Magistrates’ Court, where a judge branded Assange a “narcissist”, and faces up to a year in jail when he is sentenced at a later date.
Lawyers say the US extradition fight could last for years, given that his previous battle against extradition to Sweden to face rape allegations took 18 months.
Officials in Ecuador have also announced that an individual with alleged links to Assange was arrested while trying to board a flight to Japan on Thursday.
The man, said to be Swedish software developer Ola Bini, was held at Quito airport on suspicion of conspiring against the government, according to interior minister Maria Paula Romo.
Ms Romo told CNN’s Spanish service: “We have information on how WikiLeaks would have intervened in domestic politics.
“Today a collaborator close to Julian Assange was arrested for investigative purposes. He has been living in Ecuador and was preparing to travel to Japan.”
A tweet posted under the Twitter handle olabini on Thursday referred to a press conference given by Ms Paula Romo in which she claimed there were “Russian hackers in Ecuador”.
“Very worrisome news – this seems like a witch hunt to me,” said another tweet on the account.
Ecuador’s ambassador to the UK, Jaime Marchan, said that Assange had been disrespectful, “continually a problem” and interfered in elections, politics and the internal affairs of other countries during his stay at the embassy.