The warrant was issued when the Wikileaks founder breached bail conditions by seeking asylum in Ecuador's embassy in London. However, the British police could arrest Assange if he leaves the embassy, for breaching his bail conditions when he sought refuge there, Reuters said.
However, the court announced on Tuesday his application had been rejected.
"I'm not persuaded that the warrant should be withdrawn", Judge Emma Arbuthnot said in her ruling.
The reason Assange is unlikely to head straight out the door to the nearest Starbucks is that there may be a USA indictment hanging over him for his decision to leak classified documents.
Swedish prosecutors had already dropped their investigation over sexual assault and rape allegations, which he denies. A decision in Assange's favor would end Britain's case against him.
Assange only very rarely emerges on the balcony of the embassy building, citing concerns for his personal safety, but frequently takes part in media conferences and campaigns via video link. Last year, WikiLeaks released documents detailing US government hacking tools.
Assange's supporters say his health has deteriorated significantly during his years living in the embassy and the court has heard about Assange's depression, dental, and shoulder problems.
US officials haven't confirmed whether a request for Assange's extradition has been made.
That apprehension related to "what might happen to him in America as a result of extant legal procedures" as well as "what has happened to others", Mr Summers said.
"Once at court, the defendant would be given the opportunity to explain his failure to surrender and that is when Mr Assange would be able to place before the court his reasonable cause for failing to do so".