The matter was heard in chambers because the psychiatric evaluation of Martin Keevy, 47, at the Free State Psychiatric Complex had not yet been completed.
Keevy was sent to the complex for a 30-day evaluation about a month ago.
The matter was postponed to 2 July.
Keevy, Hein Boonzaaier, 50, Johan Prinsloo, 49 and Mark Trollip, 49, were arrested on 16 December.
They are accused of planning to kill ANCs leaders by detonating a bomb at the party's national elective conference in Mangaung.
Magistrate Mziwonke Hinxa denied Keevy, Trollip, and Prinsloo bail in January.
Boonzaaier was granted R80 000 bail.
Trollip, Prinsloo, and Boonzaaier were expected to appear in court again in August.