A bench headed by justice BS Chauhan directed the Centre to end the logjam in the issue in which ministries of law, home affairs and external affairs are involved and make its stand clear on February 10.
"Will you be able to end the logjam by next Monday? Don't expect us to grant adjournment on the next date," the bench said while posting the case for hearing on February 10.
Attorney general Goolam E Vahanvati told the bench that the Centre has "almost" resolved the issue and will respond on the next date of hearing.
Senior advocate Mukul Rohatgi, appearing for Italian Government and Marines, submitted that the Centre has not been able to proceed in the case and 13 months have lapsed since the apex court has passed the order for conducting day-to-day proceedings.
He submitted that marines should be allowed to go back to their country.
The bench was hearing a petition filed by Italian government challenging invoking of anti-terrorism law SUA (Suppression of Unlawful Acts against safety of Maritime Navigation And Fixed Platforms on Continental Shelf) Act, saying it is against the order of the apex court which allowed proceedings only under the Maritime Zone Act, IPC, CrPC and UNCLOS.
The joint petition, filed by Ambassador of Italy Daniele Mancini along with Italian marines Massimiliano Latorre and Salvatore Girone, also sought direction to the Centre and NIA to expedite the proceedings in the case or discharge the marines.
Read: Italy wants Marines case to be solved, says special envoy
During the last hearing on January 20, the apex court had adjourned the case after Vahanvati had submitted that the Centre was trying to resolve all disputes with Italian government on the issue.
The petition has said, "Invoking the anti-terrorism SUA Act would tantamount to the Republic of Italy being termed a terrorist state and acts of its organs, which were in repression of piracy, as being deemed as acts of terrorism, which is wholly untenable and unacceptable in the facts and circumstances of this case and in keeping with the comity of nations and international cooperation."
It has said that the draft protocol of 2005 to the SUA convention expressly excludes the applicability of the convention to activities undertaken by the military forces of a State in the exercise of their official duties.
"The purported attempt by the Centre to unilaterally invoke the provisions of SUA Act is contrary to and in wilful disregard of the directions of this court," the petition has said, adding that they came to know about invoking SUA on the basis of application filed by NIA in trial court.
It has contended that one year has passed since the apex court had directed an expeditious hearing in the case but the Centre has failed to implement the order and charge sheet has so far not been filed in the case.
"The petitioners have been detained in India for the last two years without any criminal case against them being started and the Centre has in fact failed to present any Final Report against them for almost one year despite the direction of the apex court to try and dispose of the case on a fast track basis," the petition has said, adding that the accused be allowed to return to Italy till the proceedings begin.
On January 18 last year, the Supreme Court had directed the central agency to probe the case against the marines and directed the Centre to set up a special court to conduct the trial on a day-to-day basis after the charge sheet is filed.
The case pertains to the killing of two Indian fishermen allegedly by Latorre and Girone on board 'Enrica Lexie'.
Fearing a pirate attack, the two officers had allegedly fired at the fishermen's vessel off Kerala coast on February 15, 2012, killing two of them. The marines were arrested on February 19, 2012.