In the last hearing, the court said it had received a report of the three-member mediation panel, headed by former apex court judge F.M.I. Kalifulla, and took on record the contents.
The other two members of the panel are spiritual guru Sri Sri Ravi Shankar and senior advocate Sriram Panchu.
The court has barred publication of the report's contents as the panel will continue the mediation process till the end of the month.
The top court had on March 8 appointed the three-member panel to talk to all stakeholders and try to reach a consensus to resolve the Ayodhya row.
Recommending mediation, the court had said it was looking for "a possibility of healing relationships". It expected mediation to succeed in developing a consensus on the sensitive matter. It asked the panel to conduct in-camera proceedings.