The judge blocked the request because of concerns over Mr Assange’s mental health and risk of suicide in the US.
The 49-year-old is wanted over the publication of thousands of classified documents in 2010 and 2011.
The US claims the leaks broke the law and endangered lives. Mr Assange has fought the extradition and says the case is politically motivated.
The US authorities have 14 days in which to lodge an appeal and are expected to do so. This means Mr Assange is not likely to be freed from London’s Belmarsh Prison – where he is being held – immediately.
YouTube video provided courtesy of BBC News