"Mr Assange failed to surrender to custody".
He tweeted that 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.
Senior District Judge Emma Arbuthnot said at Westminster Magistrates' Court on Tuesday that she was not persuaded that the warrant should be withdrawn, despite the argument he still has no objective.
"Having considered the arguments set out above (and by agreement at this stage not having considered the public interest arguments [.]) I am not persuaded that the warrant should be withdrawn".
Assange, 46, absconded in 2012 to enter the Ecuadorian embassy, to avoid extradition to Sweden over allegations of sexual assault and rape. The Swedish case has since been dropped.
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.
Mr Assange's lawyers went to court last month to argue that the British warrant serves no goal because he is no longer wanted for questioning.
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He said Assange had been living in conditions "akin to imprisonment" and his "psychological health" has deteriorated and was "in serious peril".
However, Aaron Watkins, who represents the Crown Prosecution Service (CPS), called Summers' argument "strange and untenable", adding that it was an attempt at "contorting legislation" to allow Assange to leave the embassy.
"Failing to surrender to bail is like insulting the court's authority" and unlikely to go down well with the court, she said.
Assange could face charges in the United States that include espionage, conspiracy and theft, according to Wikileaks.
Months later Swedish authorities sought to question him about an allegation of rape which he denied.
Snow and ice warning extended
Forecasts for severe cold have triggered a government "weather action" health alert - one step below "national emergency". Aberdeen, Glasgow and Edinburgh, all 1-4, seem certain to be doused in snow by the end of the week, the bookies said.