British Judge Emma Arbuthnot said she was "not persuaded" the warrant should be withdrawn, according to the AP.
A European Arrest Warrant was issued for the Australian, but after Swedish prosecutors dropped their investigation previous year Mr Assange's lawyers applied for the withdrawal of the warrant claiming that it had "lost its objective and its function".
The Metropolitan Police Service (MPS) said the incident was "stood down" after the package was assessed.
The reason Assange is unlikely to head straight out the door to the nearest Starbucks is that there may be a U.S. indictment hanging over him for his decision to leak classified documents.
The judge agreed that Assange's legal team could make a public-interest argument and set another hearing on the matter for February 13. She said he would be able to argue his case and "put an argument for reasonable cause" for breaching his bail conditions.
"His health issues are not that bad", said Arbuthnot.
There are no formal charges in against Assange in the USA, though news reports previous year suggested the Justice Department was looking into it.
North Korea slams USA sanctions as wild violation of int'l law
China's support for increasingly tough United Nations sanctions has also sparked a backlash from Pyongyang. State Department spokesman said: 'It's clear that Russian Federation needs to do more .
USA officials haven't confirmed whether a request for Assange's extradition has been made.
Assange has been staying - virtually imprisoned, he says - at the Ecuadoran Embassy for five years.
The British Foreign Office last month rejected Ecuador's request to grant diplomatic status to Assange, which would have given him immunity from arrest. However, with the arrest warrant upheld, Assange can't step onto the streets of London without risking arrest.
This afternoon, Mr Assange claimed reports he had lost the appeal were "fake news" and said the hearing was still going on, with three other points yet to be decided.
She told the court that not surrendering to bail was a stand-alone offence under the Bail Act and Mr Assange must explain why he had failed to do so.