A bench comprising Justices PC Ghose and RF Nariman asked all the parties in the case to file their written arguments by April 6 and posted the matter for further hearing on April 7. Yesterday, the Supreme Court had adjourned the matter for today as Justice Nariman was not present.
The top court will decide whether conspiracy charges will be revived against Mr Advani, 89, and other leaders like Murli Manohar Joshi and Union Minister Uma Bharti. The charge was dropped by lower courts. In the previous hearing earlier this month, the Supreme Court had said it would not accept the discharge of BJP leaders on technical grounds.
Earlier this week, the court suggested an out of court settlement to resolve what it called a "sensitive and sentimental issue". The Chief Justice of India, JS Khehar, even said he is ready to mediate.
Mr Advani's lawyer had told the Supreme Court that if conspiracy charges are added, then 183 witnesses who had testified in a lower court would have to be called again.
Today, the BJP leaders' lawyer sought permission from the court for appearing before another bench in a part-heard matter.
Mr Advani, Mr Joshi and a dozen others including Vinay Katiyar and Kalyan Singh were freed by a court in Raebareli of conspiracy charges in the razing of the 16th century Babri mosque in Ayodhya in December 1992 by Hindu activists who believed it was built on the birthplace of Lord Ram.
The Supreme Court, in 2011, had stayed the Allahabad High Court order. The verdict said the site of Babri mosque is to be divided into three parts, each going to Nirmohi Akhara, Ram Lalla and the Sunni Central Waqf Board of Uttar Pradesh.