It was issued in 2012 for jumping bail.
British Judge Emma Arbuthnot said she was "not persuaded" the warrant should be withdrawn, according to the AP.
Mr Assange's team argued the United Kingdom warrant should be withdrawn as it "lost its goal and function".
Olivia Harris / Reuters Julian Assange has been living at the Ecuadorian embassy in London since 2012, the year he is pictured here. Sweden had chose to drop its arrest warrant in 2012, but emails uncovered by an Italian journalist's Freedom of Information request had revealed that a British prosecution lawyer persuaded them to insist that Assange leave the embassy.
Outside court, Assange's lawyer Jennifer Robinson said whether or not the warrant is quashed Assange would not leave the embassy until he had an assurance he wouldn't be extradited to the US.
She said that whistleblower had committed an offence under the Bail Act by refusing to surrender to bail and must explain why he failed to do so.
Assange's lawyer told a judge that the warrant had "lost its objective and its function" due to the dropping of the Swedish charges.
"His health issues are not that bad", said Arbuthnot.
Ecuador, which made Assange an Ecuadorian citizen last month, has urged the United Kingdom to grant him diplomatic status so that he may leave the embassy without fearing arrest.
Assange has denied the allegations of sexual misconduct in Sweden - he claimed the sex was consensual - but he has long argued that there is an worldwide effort led by Washington to persecute him for his role in the publication of hundreds of thousands of classified USA government documents, diplomatic cables and emails. He fears he will immediately be taken into custody if he leaves the embassy, sparking what would likely be a long legal battle against extradition to the U.S.
Donald Trump's newly appointed attorney general Jeff Sessions has declared the arrest of Assange a "priority". "This is and has always been our overriding concern".
Julian Assange's lawyer Jennifer Robinson speaks outside court on Tuesday. Earlier this month, he was granted Ecuadorean citizenship.
Mr Assange was interviewed in November 2016 at the Ecuadorian embassy and the interview was relayed to Swedish prosecutors.
British prosecutors had opposed the removal of the warrant, saying Assange shouldn't be immune from the law simply because he has managed to evade justice for a long time.
When asked if a successful ruling would mean Assange was free to leave the embassy, a CPS spokesman said: "Hypothetically yes, that would be our interpretation".