The move followed an order by the Hamburg-based International Tribunal for the Law of the Sea on Monday.
In a case that sparked a bitter diplomatic row between Italy and India, the court also rejected Italy's appeal for the marines to be freed pending the final ruling.
India's Supreme Court said on Wednesday that all proceedings against the marines would be suspended until January 13th.
Massimiliano Latorre and Salvatore Girone are accused of firing shots which killed the Indians while they were fishing off the southern Indian state.
They were on board an Italian oil tanker, providing protection as part of an international anti-piracy mission.
Latorre was last year allowed to temporarily return to Italy for medical treatment after he suffered a blood blockage in his brain. His permission to remain in Italy for recuperation was extended by six months in July.
Girone has been living at Italy's embassy in New Delhi.
The detention of the marines and the long delay in the case coming to trial is a sore subject in Italy, with Prime Minister Matteo Renzi's government frequently being flayed by the opposition over its failure to bring both men home.
Italy argues that because the shooting took place in international waters, the men should be tried at home, but India wants them tried in an Indian court.