Lawyers for Assange argued in a London courtroom that the outstanding British warrant, issued after Assange skipped bail, had "lost its goal and function" following Sweden's decision past year to drop an investigation into sexual assault allegations.
Assange has been hiding in the Ecuadorian Embassy in London for the last five years, having claimed asylum to evade extradition to face rape allegations in Sweden.
Chief Magistrate Emma Arbuthnot said legal precedents "underline the importance of a defendant attending court when bail to do so", adding: "I am not persuaded that the warrant should be withdrawn". (AAP) Julian Assange has sought refuge in the Ecuadorian embassy since 2012.
Last year, Sweden dropped its investigation into rape allegations against Assange because it was unable to get access to him.
The whistleblower took his appeal to Westminster Magistrates Court, with the Crown Prosecution Service (CPS) saying that "hypothetically" Assange would be free to leave the embassy and not face arrest by British police if he was successful.
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In April 2017, US Attorney General Jeff Sessions said arresting Julian Assange over Wikileak's publishing activities was a "priority".
His supporters hope that a court victory will force the British authorities to disclose whether such a warrant has been issued by the USA authorities.
London police responded to reports of a suspicious package at Ecuador's embassy in the city on Tuesday. That investigation was dropped past year after the prosecutor said leads had been exhausted. She said the Ecuadorean government is seeking a "dignified and just" solution in his case with the British government.
But prosecutor Aaron Watkins earlier called Assange's court bid "absurd".
"In order to proceed with the case, Julian Assange would have to be formally notified of the criminal suspicions against him".