The marines, Massimiliano Latorre and Salvatore Girone, are accused of killings two Indian fishermen off the Kerala coast in 2012.
"Petitioners (Latorre and Girone) shall be liable to adhere to the time schedules fixed in relation to hearing before the international arbitral tribunal," the bench also comprising Justices D Y Chandrachud and S K Kaul said, adding that the final award of the tribunal be put up before it.
The court, meanwhile, asked Additional Solicitor General P S Narsimha, appearing for the centre, to keep the Kerala government informed about the developments which may take place from time to time before the tribunal.
On September 28, 2016 the top court had allowed Latorre to remain in his country till the international arbitraltribunal decides the jurisdictional issue.
The top court had said all the conditions which were imposed on Girone would be applicable on Latorre as well besides putting a condition on the government to submit to it the three-monthly report about the case's progress at the tribunal.
The court's direction had come on a plea by Italy seeking modification of bail conditions of Latorre to enable him to remain in that country till jurisdictional issue was decided by the international tribunal.
The top court had on September 8, 2016 decided to hear Italy's plea on behalf of Latorre who had sought urgent hearing on the ground that an earlier court order was valid till September 30, 2016.
While relaxing Girone's bail conditions on May 26, the top court had allowed him to go to his country till the jurisdiction issue was decided.