NEW DELHI—India's Supreme Court sought Thursday to restrain Italy's ambassador from leaving the country in response to Rome's declaration that two Italian marines won't return to India to stand trial on murder charges.

The marines, Massimiliano Latorre and Salvatore Girone, are accused of shooting and killing two Indian fishermen off the coastal state Kerala in February 2012. The men, who deny they committed murder, have spent part of the past year in custody in India.

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