Indian prosecutors alleged the two marines shot and killed the two fishermen in February 2012.
Italy now says the two marines won't be returning to India to face trial as agreed.
The court also asked the two marines to return to India to attend Monday's hearing.
Still, Italy appeared to bow to the pressure, sending the two marines back to India late last month.
The two Marines spent four hours in the ocean before they were rescued.
He said he personally opposed the Italian decision to send the two marines to New Delhi last week for prosecution.
Chris Stevens, along with the two Marines and another who were murdered along with him, had volunteered to serve his country.
India rejected these calls, urging Italy to respect the assurance given to the Supreme Court and return the two marines as promised.
At the time, Italy vowed the two marines would return to India.
What makes Italy's position more complicated is the personal assurance Mr Mancini gave to the Indian Supreme Court that the two marines would return.
Italy now says the two marines won't be returning to India to face trial as agreed, a move that sparked angry reactions from India.
It hasn't helped that the two marines were welcomed home by Italian Prime Minister Mario Monti, looking like "heroes", says former foreign secretary Kanwal Sibal.
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Italy now says the two marines will not be returning to India to face trial as agreed, a move that sparked angry reactions from India.
Another two Marines and three civilians also were wounded in the attack, which occurred in Baaj, in the northern province of Nineveh, the military said.
Mukul Rohatgi, a lawyer representing the two marines and the government of Italy, said in an interview they would oppose transferring the case to the agency.
Authorities recovered the bodies of two civilians on Wednesday, after previously confirming the deaths of two marines and wounding of 18 other people during the attack.
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"The position of the government of Italy regarding the two marines is not acceptable to us, " Indian Foreign Secretary Ranjan Mathai told reporters after the meeting.
It follows a Supreme Court order to Mr Mancini not to leave India after Rome's refusal to return two marines charged with the murder of two fishermen.
In India, the two marines are being kept in the custody of the Italian embassy, an arrangement that was in place before they left India last month.
In its notice Thursday, issued in response to Mr. Swamy's petition, the Supreme Court also requested the two marines to return to India to attend Monday's hearing.
Mukul Rohatgi, a lawyer representing the two marines and the government of Italy, said in an interview that they would oppose transferring the case to the National Investigation Agency.
Italy's decision to send back to Delhi for trial two marines accused of murdering two Indian fishermen is being described by many in India as a triumph for its diplomacy.
When the two marines arrive in India, they will be kept in the custody of the Italian embassy, said Mr. Khurshid, an arrangement that was in place before they left India last month.
India's Attorney General GE Vahanvati told the judges that Rome's failure to return the two marines "is a breach of undertaking given to the highest court of the land and the government is extremely concerned about it".
Two Italian marines accused of murdering two Indian fishermen, in a case that has sparked a diplomatic row, are to be sent back to Delhi for trial.
India's Supreme Court has allowed an anti-terror agency to probe the case of two Italian marines accused of killing two Indian fishermen in a case that sparked a diplomatic row.
Italian Foreign Minister Giulio Terzi has resigned in protest of his government's decision to send two Italian marines, accused of killing two Indian fishermen, to Delhi for trial.
Two Italian marines, charged in India with the murder of two fishermen, will not be returning to India to face trial, Italy's foreign ministry says.
The statement said the decision to pardon Col Romano was inspired by the same principle that Italy hoped to see used in the case of two Italian marines facing murder charges in India over the shooting of two fishermen.
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Two Italian marines have been charged by an Indian court with shooting dead the two fishermen, but the trial has yet to formally start amid bickering between Italy and India over jurisdiction.
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