The five-judge Constitution Bench of Chief Justice Ranjan Gogoi, Justice S.A. Bobde, Justice D.Y. Chandrachud, Justice Ashok Bhushan and Justice S. Abdul Nazeer reserved the order after hearing various contesting parties.
Hindu bodies except Nirmohi Akhara have opposed the suggestion of the apex court to refer the issue for mediation, while Muslim bodies have supported it.
Hindu bodies like Nirmohi Akhara suggested the names of Justices (retd) Kurian Joseph, AK Patnaik and GS Singhvi as mediators, while the Hindu Mahasabha faction of Swami Chakrapani proposed the names of former CJIs Justices J S Khehar and Dipak Misra and Justice (retd) A K Patnaik to the bench.
The apex court in its Wednesday hearing had observed that primarily the issue is not about 1,500 square feet land, but about religious sentiments.
The bench had said it was conscious of the gravity and impact of the issue on "public sentiment" and also on "body politics of the country".
It has also said that the judges were aware of the history and was seeing that the dispute be resolved amicably as "It is not only about property. It is about mind, heart and healing, if possible."
The bench had also said it was not appropriate to pre-judge that the mediation would fail and people would not agree with the decision.
The court is hearing of a batch of cross petitions challenging the 2010 Allahabad High Court verdict trifurcating the disputed site.
Fourteen appeals have been filed in the apex court against the Allahabad High Court judgment, delivered in four civil suits, that the 2.77-acre land in Ayodhya be partitioned equally among the three parties -- the Sunni Waqf Board, the Nirmohi Akhara and Ram Lalla.
(With inputs from agencies)