The other marine Massimiliano Latorre is already in Italy on health grounds and his stay there was recently extended by the apex court till September 30 this year.
A vacation bench of Justices P C Pant and D Y Chandrachud sought a fresh undertaking from Italian Ambassador here stating that if the International Arbitral Tribunal (IAT) decides jurisdictional issue in India's favour then he will be responsible in bringing back the marine within one month.
It also said the marine will not tamper with any evidence nor influence any witness in the case.
The third condition imposed was that Girone will give an undertaking that he will remain under the jurisdiction of Supreme Court.
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Lastly, if found violating any of the conditions imposed, his bail will be cancelled, the apex court said.
During the hearing, Additional Solicitor General (ASG) P S Narasimha said that Centre has no objection to the application moved by Girone if he complies with the conditions imposed by the apex court.
Girone, who presently is in the custody of the apex court and residing in Italian embassy here, had filed the application through lawyer Jagjit Singh Chhabra, also seeking a direction that Ministry of Home Affairs and the Foreigners Regional Registration Office be asked to provide him with the "necessary residential permit and exit visa".
The marines, who were on board ship 'Enrica Lexie', are accused of killing two Indian fishermen off the Kerala coast on February 15, 2012.