Julian Assange was too ill to appear at his court hearing in London, his lawyers said.
The 47-year-old had been expected to appear at Westminster Magistrates' Court via video link from Belmarsh Prison in his fight against extradition to the United States over allegations that he conspired to break into a classified Pentagon computer.
Assange did not appear at the five-minute hearing on Thursday, with his lawyer Gareth Peirce saying he was "not very well".
Chief magistrate Emma Arbuthnot set a date of June 12 for the next hearing, saying it will be held at Belmarsh prison.
A Julian Assange supporter, dressed as a giant whistle, outside Westminster Magistrates Court
The public gallery was filled with Assange supporters, with many having queued outside the court building for more than an hour.
Among them was journalist and BAFTA-winning documentary maker John Pilger, who said he is friends with Assange.
Asked about Assange's health, Mr Pilger said: "He needs a great deal of diagnostic care and rehabilitation. He's gone through an extraordinary physical and mental ordeal. And now he's having to go through this.
"This is so shameful, so shameful that we are even here today to consider the extradition of a journalist for trying to protect his sources."
The WikiLeaks founder was set to appear in court via video link on Thursday
Just a few hours before the case management hearing, WikiLeaks said it has "grave concerns about the state of health of our publisher, Julian Assange, who has been moved to the health ward of Belmarsh prison".
A spokesman added: "During the seven weeks in Belmarsh his health has continued to deteriorate and he has dramatically lost weight. The decision of the prison authorities to move him into the health ward speaks for itself.
"We strongly condemn the refusal by the Swedish court to postpone a hearing on 3rd June on the basis of Mr Assange's health condition.”
Also this month, an investigation into rape allegations against Assange, which he denies, has been reopened by Swedish prosecutors who have requested Uppsala District Court detains him in his absence.
Deputy director of public prosecution Eva-Marie Persson said if the court decides to detain Assange, she "will issue a European Arrest Warrant concerning surrender to Sweden".
Assange is serving a 50-week sentence in Belmarsh Prison for bail violations.