Judge Emma Arbuthnot said a more substantive extradition hearing set for June 12 may be moved to a court next to Belmarsh Prison for convenience.
Roughly two dozen supporters chanted "Free Assange" outside the courthouse. His case has attracted fresh support from free press advocates in the week since the US filed serious espionage charges against him.
He had earlier been held on suspicion of conspiracy to break into classified computer systems, a less serious charge.
WikiLeaks said in a statement it has "grave concerns" about Assange's health. The anti-secrecy group says he has been moved to the prison health ward.
The group says Assange has "dramatically lost weight" and recently "it was not possible to conduct a normal conversation with him".
The complicated extradition process, which involves both Sweden and the US and deals with press freedom and national security issues, is expected to last for months or years.
Assange was arrested by British police in April after Ecuadorean officials withdrew his asylum status. He had sought refuge in the Ecuadorean Embassy in 2012 when Sweden was trying to question him about sexual misconduct allegations.
- AP