The two, Massimiliano Latorre and Salvatore Girone, had been granted a special leave last month by an Indian court to return to Italy to vote in elections but had skipped bail.
The government said on Thursday it had received "ample assurances" from Indian authorities "on the treatment that the marines will receive and the defence of their fundamental rights".
"The government decided, also in the interests of the marines, to maintain the commitment taken when they were granted leave to take part in the elections to return to India by March 22," it said.
"The marines agreed to this decision," it added.
Prime Minister Mario Monti met with Defence Minister Giampaolo Di Paola and Steffan de Mistura, a junior foreign minister who has taken a lead on the case, to discuss the issue on Thursday.
The government had announced on March 11 that the marines would not return from their leave.
The two are accused of killing two fishermen they mistook for pirates off the port of Kochi last year while they were serving as security guards on an Italian oil tanker.