The court postponed today's hearing as Satish Pradhan, one of the six accused, did not appear before it.
On May 20, the special CBI court began day-to-day hearing in the politically sensitive case and granted bail to the five VHP leaders named as accused in it.
The Supreme Court had on April 19 directed the special court to start proceedings in the matter within a month and deliver its verdict within two years.
The CBI court had earlier issued summons to six accused persons, of whom five including Ram Vilas Vedanti (59) appeared in the court and sought bail.
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Besides Vedanti, those who appeared in the CBI court on Saturday were VHP leaders Champat Rai (71), Baikunth Lal Sharma (88), Mahant Nritya Gopal Das (79) and Dharmdas Maharaj (68).
That day too, Pradhan, the sixth accused, did not appear.
The Supreme Court had last month directed that senior BJP leaders, including L K Advani, Murli Manohar Joshi and Uma Bharti, will face trial on conspiracy charges in the Ayodhya case.