Lawyers for Massimiliano Latorre and Salvatore Girone filed a petition in the Supreme Court requesting that the case be dismissed so they can return to Italy because of the "failure of [the Indian] government to file a report for almost a year".
The petition is the latest twist in a case which dates back to February 2012 and sparked a diplomatic row between the two countries.
India's National Investigation Agency has filed preliminary charges of murder and attempted murder against the marines for allegedly shooting dead two fishermen off the southern coast of Kerala.
But formal charges have not been laid against the pair and the Italian government is concerned a trial would get bogged down in India's slow legal system.
Citing the delay, the petition requests the court to "close the right of the government to file a charge sheet" and "permit the marines to travel to Italy".
The marines were guarding an Italian oil tanker in February 2012 when they opened fire on a fishing boat and two fishermen were killed. The marines say they mistook the fishing boat for a pirate vessel.
They were allowed to go home to vote in elections and returned to India for trial in March last year.
Rome initially refused to send them back to India, triggering a bitter diplomatic stand-off between the two countries.
Italy had insisted the pair should be prosecuted in their home country because it said the shootings involved an Italian-flagged vessel in international waters. India says the killings took place in waters under its jurisdiction.
India, which uses the death penalty in what it says are the "rarest of rare cases", has assured Italy that the two men would not face execution if found guilty.
The return of the two marines to India caused huge controversy in Rome and prompted Italy's foreign minister to resign in protest.
India told Italy in April last year that preparations to set up a special court to try the pair were at an "advanced stage".