Assange, 46, has been holed up inside the Ecuadorean embassy in London for more than five years because he fears extradition to the United States.
If he were to leave, he would face arrest by British police for skipping bail in June 2012 by seeking refuge in the embassy to avoid extradition to Sweden to face an allegation of rape, which he denied.
The Swedish case has since been dropped but in the eyes of the British authorities Assange remains in breach of his bail conditions.
Assange has said he feared Sweden would hand him over to the United States to face prosecution over WikiLeaks' publication of a large trove of classified military and diplomatic documents - one of the largest information leaks in U.S. history.
His lawyer told a hearing at London's Westminster Magistrates' Court last week that the UK arrest warrant issued for breaching bail conditions should be dropped because Swedish prosecutors had dropped their investigation and withdrawn their bid to have him extradited.
However, the court announced on Tuesday his application had been rejected.
After the decision, Assange's lawyer Mark Summers asked her to consider whether it would be in the public interest to continue pursuing his client for breach of bail conditions.
Arbuthnot said normally such issues would only be considered if somebody were brought to court to explain their failure to surrender to bail.
Summers replied: "There are exceptional circumstances."
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