The court was responding to litigation seeking daily hearings in a long-running case about the disputed site in the northern town of Ayodhya.
Hindu mobs destroyed a 16th Century mosque at the site in 1992, sparking riots that killed nearly 2,000 people.
Hindus want a temple to be built at the site, while Muslims want a new mosque.
Hindus claim the mosque was the birthplace of one of their most revered deities, Lord Ram, and that it was built after the destruction of a Hindu temple by a Muslim invader in the 16th Century.
Chief Justice JS Khehar said "such sensitive matters" needed to be resolved through negotiations. He also offered to act as a mediator between the two parties.
The court has been sporadically hearing the case since 2011 after setting aside a lower court's order which in a 8,500-page judgement said that two-thirds of the disputed site should be allocated to Hindu groups, with the remainder going to Muslims.
The Allahabad High Court's ruling in September 2010 addressed three major issues. It said the disputed spot was the Hindu God Ram's birthplace, that the mosque had been built after the demolition of a temple and that it was not built in accordance with the tenets of Islam.
For the first time in a judicial ruling, it also said that the disputed site was the birthplace of the Hindu god.
But both parties appealed against the order in the Supreme Court.
The case has already languished in India's famously sluggish legal system for so long that most of the original petitioners have died.
India's Supreme Court has advised Hindus and Muslim to settle a bitter dispute over a controversial religious site through negotiations.