Susan Benn of the Julian Assange Defense Fund said Assange, who has been at the embassy more than a week, would stay there while his application for political asylum was processed, The Guardian reported.
The Metropolitan Police requested in a letter that Assange, a citizen of Australia, surrender at 11:30 a.m. Friday.
Benn said Assange had been advised not to comply with the police request.
"This should not be considered any sign of disrespect," Benn said. "Under both international and domestic U.K. law, asylum assessments take priority over extradition claims."
Swedish authorities want to question Assange concerning allegations of sexual assault and rape in Stockholm in 2010. Assange has said the sexual relations were consensual and called the allegations politically motivated.
Benn said Assange "did not feel safe" from being extradited from the United Kingdom to the United States over leaked diplomatic cables.
"It is only a matter of time before U.S. authorities begin extradition proceedings against Julian and other leading members of WikiLeaks on various charges, including conspiracy to commit espionage," Benn said. "It is clear that there is a legal process in place which will result in taking Julian to the U.S., which if allowed to succeed, would violate his basic rights."
She said Swedish officials have refused "without reason" to travel to London to interview Assange, "causing him to be trapped in the U.K. under virtual house arrest."
The British Supreme Court has upheld a ruling that Assange's extradition to Sweden was legal.