His lawyers were basing their request on a February 5 non-binding legal opinion of the UN Working Group on Arbitrary Detention, which said Assange's confinement amounted to an arbitrary detention by Sweden and Britain.
"I think (the opinion of the UN working group) is an important fact and should be taken into account," Tomas Olsson, a lawyer for Assange, told AFP.
"We want them to retry the decision and overrule it," he said.
Appeals to have the warrant dropped were also denied.
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Swedish authorities want to speak to Assange about the rape allegation dating back to 2010 and whose statute of limitations does not expire until 2020.
Assange has lived at the embassy since 2012, in a small office room with a bed, computer, sun lamp, treadmill and access to a small balcony decorated with Ecuador's flag.
Assange fears that if he were sent to Sweden, he could be extradited to the United States to be tried over the publication of hundreds of thousands of classified documents.
Both Britain and Sweden have angrily disputed the group's findings.
Founded by Assange in 2006, WikiLeaks has infuriated the United States by releasing some 500,000 secret military files on the wars in Afghanistan and Iraq and 250,000 diplomatic cables.