The apex court also urged the mediators to continue the court-monitored process confidentially till July 31 as it would apparently enable the top court to pass further orders.
The report will be submitted in the apex court on August 1. If required, the Supreme Court will tentatively fix the hearing of appeals on the Ayodhya issue from August 2.
The top court said that it had received a report of three-member mediation panel headed by former apex court judge F.M.I. Kalifulla and it also took on record the contents of the report furnished before the court.
The court has already barred the contents of the report from being made public as the panel will continue with the mediation process till this month end.
Earlier, the court had tentatively fixed July 25 for commencement of day to day hearing on appeals in the Ayodhya land dispute case. The court observed that hearing would be conducted if it felt the mediation had been inconclusive.
The top court, on March 8, took a major step as it appointed a three-member mediation panel to talk to all stakeholders and try to reach a consensus on solving the vexed dispute.
The committee has been asked to file a status report on Thursday, against the backdrop of pleas for speedy trial.
The court, while recommending mediation, said it was looking for "a possibility of healing relationships".
It expected the mediation to succeed in developing a consensus on the sensitive matter.
Headed by Kalifulla, the panel was tasked to hold consultations to explore the potential to reach an amicable settlement.
The other two members of the panel are spiritual guru and founder of Art of Living Foundation Sri Sri Ravi Shankar and senior advocate Sriram Panchu, a well known mediator in legal circles.
The Supreme Court asked the panel to conduct in-camera proceedings and the complete the mediation process within eight weeks.
The court stressed on maintaining confidentiality on the proceedings as it will protect the ongoing dialogue from unwarranted controversies and unsolicited comments.
The Hindu parties have contested that the mediation is not progressing in a positive direction while the Muslim parties have held back from making a statement on the nature of the proceedings.
As a result, the court has asked the mediation committee to submit its report on the consultations held so far.
( With inputs from IANS )