Assange's lawyer Mark Summers had argued in court last week that the warrant had "lost its goal and its function".
The outstanding warrant stands from 2012, which is in connections with the Swedish investigation, even through it was closed down a year ago.
"I'm not persuaded that the warrant should be withdrawn", Judge Emma Arbuthnot said in her ruling.
Judge Arbuthnot rejected a legal argument to have the arrest warrant against him quashed on the basis that with the Swedish case dropped there was no longer any justification for it.More news: Liverpool coach delivers verdict on new signing Tony Gallacher's under-23 debut
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.
The UK government recently refused to grant Mr Assange diplomatic status, calling him to leave the Ecuadorean embassy to "face justice" with no guarantee that he will not be extradited to the US.
The Wikileaks founder has consistently denied the allegations of rape and sexual assault.
Assange was granted political asylum in 2012 to avoid extradition to Sweden over rape allegations.
Assange sought asylum in the embassy because he feared Swedish police would eventually extradite him to the United States, where he could face decades in jail over WikiLeaks' publication of thousands of secret military documents in 2010.More news: Lauda calls for F1 to reverse grid girl decision
An attorney for Assange told a district judge since the Swedish case had been dropped, the warrant had "lost its objective and its function".
"The proper approach is that when a discrete, standalone offence of failing to surrender occurs, it always remains open to this court to secure the arrest", he said.
Swedish prosecutors dropped the case a year ago, saying all possible leads had been "exhausted".
Had the judge ruled in Assange's favor on Tuesday, he would have been free to leave the embassy without being arrested on the British warrant.More news: EFF calls for secret ballot in motion of no confidence on Zuma