NEW DELHI—Indian Prime Minister Manmohan Singh said that there would be consequences if Rome doesn't return two Italian marines accused of killing two Indian fishermen to face trial in India.

The marines, Massimiliano Latorre and Salvatore Girone, are accused of fatally shooting two Indian fishermen off the coast of the Indian state of Kerala last year. Police in Kerala detained the two officers, who deny they committed murder, triggering a diplomatic dispute with Italian authorities over who has jurisdiction in the criminal...