Even if there is "one per cent chance" of settling the dispute amicably, the parties should go for mediation, a five-judge constitution bench headed by Chief Justice Ranjan Gogoi suggested.
The top court said it would pass an order on March 5 on whether to refer the matter to a court-appointed mediator.
The suggestion for mediation was mooted by one of the judges, Justice S A Bobde, during the hearing when both the Hindu and the Muslim sides were sparring over the veracity of documents related to the case which were translated by the Uttar Pradesh government and filed with the apex court registry.
"We are considering it (mediation) very seriously. You all (parties) have used the word that this matter is not adversarial. We would like to give a chance to mediation even if there is one per cent chance," said the bench, also comprising Justices Bobde, D Y Chandrachud, Ashok Bhushan and S A Nazeer.
"We would like to know your (both parties) views on it. We do not want any third party to make a comment to jeopardise the entire process," the bench said.
While some of the Muslim parties agreed to the court's suggestion on mediation, some Hindu bodies including the Ram Lalla Virajman opposed it, saying several such attempts have failed in the past.
"Do you seriously think that the entire dispute for so many years is for property? We can only decide property rights but we are considering the possibility of healing relations," the bench said.
The bench, which posted the main matter for hearing after eight weeks and directed its registry to provide translated copies of documents to the parties within six weeks to check their veracity, said it wanted to explore the possibility of mediation to utilise the time till the next date of hearing.
Senior advcoate Rajeev Dhavan, appearing for the legal heirs of original litigant M Siddiq, said they were agreeable to the "very important suggestion" of mediation but said the court should fix a time frame for mediation as the dispute was a "knotty issue".
"We will also have to fix the time frame after talking to the mediator," the bench said.
Senior advocate C S Vaidyanathan, appearing for Ram Lalla Virajman, said they did not agree for "another round of mediation" as such attempts have failed in the past.
"In the earlier mediation, it was accepted that Lord Rama was born in Ayodhya but not at this (disputed) site. Mediation has been tried not once but several times," he said.
Senior advocate Ranjit Kumar, appearing for one of the parties, said things have not worked during earlier round of mediation and "everybody wants that the matter should be decided by the Supreme Court".
"Mediation is not possible so this court should decide the matter," Kumar said.
Dhavan referred to the mediation held between 1991-93 and said, "In the larger interest, this court is saying do it (mediation) again. From our side, we are agreeable".
At the outset, the apex court said it can proceed with the hearing if there is consensus among the parties with regard to the veracity of the translated documents.
The bench referred to a report filed by the secretary general of the apex court on the status of documents pertaining to the case which said that "the record consists of 38,147 pages of which 12,814 pages are in Hindi, 18,607 pages are in English, 501 pages are in Urdu, 97 pages are in Gurumukhi, 21 pages are in Sanskrit, 86 pages are in other language scripts, 14 pages contain images and 1,729 pages are in combination of more than one language script".
The report, which was shared with the parties in the court, said 11,479 pages were required to be translated and if all eight official translators of the apex court are asked to do the job, it is likely to take about 120 working days to make the case ready for hearing.
Vaidyanathan, however, said the exercise of translation has already been conducted and the parties had raised no objections with regard to their veracity earlier.
He said it was "not appropriate" for the other side to now raise this issue as translated documnents were verified and accepted by all parties in December 2017.
Dhavan said they have not examined the translated copies of the documents filed by the Uttar Pradesh government and they have a right to examine its veracity.
"I am insisting on my right to examine it (documents)," he said, adding, "This kind of accusation (from the other side) that we do not want to argue the case is not right. We do want to argue the case. Apart from authenticity, we will also examine the documents for its relevance".
However, the bench said, "So dispute is arising between the parties about the authenticity of translated documents. We are not going to waste our time if the parties have dispute over this."
The bench said that after the hearing commences in the matter, it does not want a situation where any of the parties raises objection about veracity of the documents.
Fourteen appeals have been filed in the apex court against the 2010 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.
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