The SC also said that if parties to the case want to amicably resolve the matter through mediation, they can still go ahead with it.
As it offered to hear the case on Saturdays as well, the court at the same time said the parties to the dispute are free to find an amicable solution through mediation, if they want, and place the settlement before it.
But the top court told lawyers from both the Hindu and Muslim sides in the Ayodhya case that it wanted to conclude the day-to-day hearings by October 18 so that the judges get almost four weeks time to write the judgment.
The target date for completion of arguments assumes significance since Chief Justice Ranjan Gogoi, who is heading the five-judge Constitution bench hearing the case, is due to demit office on November 17.
"The hearing of the appeals, which is at a very advanced stage, will continue without any interruption.
"If, in the meantime, the parties desire to settle the matter(s), including, by resort to mediation by the earlier constituted mediation panel, they may do so and place the settlement before the court, if reached," the bench said in its order.
The Court on Tuesday had asked the counsels for the Hindu and Muslim parties to inform it about a tentative ‘time schedule’ for concluding their arguments.
The Constitution bench, which also comprised Justices S A Bobde, D Y Chandrachud, Ashok Bhushan and S A Nazeer, has so far heard the Ayodhya land dispute case for 26 days after it commenced the day-to-day hearing on August 6 following the failure of mediation proceedings initiated to find the amicable resolution.
As per the apex court's calendar, the bench now has 15 working days remaining to conclude the lengthy hearing by October 18. So far, Hindu parties have argued for 16 days and senior advocate Rajeev Dhavan, representing the Muslim sides, had advanced submissions for 10 days.
"Let us make a joint effort to conclude the hearing by October 18 so that we get four weeks time to write," the bench said.
Dhavan said he and his colleagues would take eight more days to conclude their submissions and two senior counsel--K Parasaran and C S Vaidyanathan--appearing for a Hindu party would need two days to rebut his arguments.
"We are open to hearing on Saturdays, if required," the bench said, adding a tentative schedule can also be worked out.
After dealing with the time schedule, the bench then said it has received a letter from former apex court judge F M I Kalifulla, who was heading the three-member mediation panel, in which it was stated that some parties have written to him for resumption of the mediation process.
"There is an ancillary issue. We have received a letter that some parties want to settle the matter by way of mediation," the bench said, adding they may do so and the proceedings before the mediation panel can remain confidential.
Referring to its earlier order, it said, "We also make it clear that the terms and the process of settlement including mediation, if resorted to, will abide by our earlier order dated March, 8, 2019, with regard to confidentiality."
While ordering the day-to-proceedings, the court had taken note of the report of the three-member panel, also comprising spiritual guru and founder of the Art of Living foundation Sri Sri Ravishankar and senior advocate and renowned mediator Sriram Panchu, that mediation proceedings, which went on for about four months, did not result in any final settlement and it had to decide the matter pending before it.
The court, which on March 8 referred the matter for mediation, had asked for in-camera proceedings to be completed within eight weeks, but later granted time till August 15 after the panel's earlier report said the mediators were ‘optimistic’ about an amicable solution.
The top court fixed the seat for mediation process in Faizabad, Uttar Pradesh, around 7 km from Ayodhya, and said adequate arrangements, including the venue of the mediation, place of stay of the mediators, their security, travel should be forthwith arranged by the state government.
It had perused a report about the progress of mediation process till July 18 and said its contents will remain confidential.
14 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.
On December 6, 1992, the Babri Masjid, constructed at the disputed site in the 16th century by Shia Muslim Mir Baqi, was demolished by kar sevaks, sparking communal riots in the country.