This is the latest twist in Assange's long legal battle to have his European arrest warrant overturned, after Sweden's Supreme Court formally agreed at the end of last month to hear his appeal.
But on Monday judges agreed to reject the bid, which was first issued in 2010 following allegations from two women in Stockholm, one who claimed rape and another who alleged sexual assault. Assange, 43, denies the accusations.
In a press statement issued on Monday morning, the court said that the arrest warrant did not violate the so called 'proportionality principle', i.e. that a restrictive legal measure needs to be in proportion to potential gains and the severity of the alleged crime.
It added that there was "a strong public interest" to investigate the alleged offences.
The court stated that although it considered the fact that the arrest warrant had been in place for a "very long time", it took the view that progress was being made in the case after Swedish prosecutors agreed to travel to London to question Assange.
"The Supreme Court notes that investigators have begun efforts to question Julian Assange in London. The Supreme Court finds no reason to lift the arrest warrant," it said in the statement.
TIMELINE: How the Assange saga has unfolded
The news comes as Swedish prosecutors are set to meet the Australian at the Ecuadorian Embassy, where he has been holed up since seeking asylum there more than two years ago.
Assange has always refused to return to Sweden to refute the allegations, fearing that Stockholm would extradite him to the US to be tried for his role in Wikileaks' publication of classified US diplomatic, military and intelligence documents.
However, Swedish prosecutors offered in March to drop their previous demand that Assange come to Sweden for questioning about the 2010 allegations, making a significant U-turn in the case that had been deadlocked for nearly five years.
Monday's high court ruling means that he could yet be sent to Stockholm as investigations continue.
Prosecutor Marianne Ny said in a press release in March that she had changed her mind about questioning Assange in London because a number of the crimes he is suspected of will be subject to 'statute of limitation' in August 2015, which refers to the maximum time after an alleged offence that legal proceedings may be initiated according to Swedish law.
The statute of limitation for the most serious offence he is accused of, rape, runs out in 2020.
"My view has always been that to perform an interview with him at the Ecuadorian embassy in London would lower the quality of the interview, and that he would need to be present in Sweden in any case should there be a trial in the future. This assessment remains unchanged," said Ny in March.
Assange's lawyer Per Samuelsson told The Local at the time that the Australian had described prosecutors' decision to question him in London as "a great victory".