The meeting was held in Italy after news media reported that the marines faced execution for killing two Indian fishermen after mistaking them for pirates, Italy's ANSA news agency reported.
The Hindustan Times said India's anti-terrorist National Investigation Agency may charge the marines, identified as Massimiliano Latorre and Salvatore Girone, under India's 2002 anti-terrorism law that calls for capital punishment for those convicted of homicide.
An official told the Hindustan Times that "there is an agreement" between government ministers to allow the move.
Italian Defense Minister Mario Mauro said he blames Indian politics for the media reports and said Italy would stand by its marines.
"It is clear that the election campaign in India is approaching in a bullying way. The Italian government will show the necessary firmness on the marines," Mauro told Italian Radio Anch'io Friday.
The reports came one day after both Indian and Italian authorities stated there was no chance Latorre and Girone would receive the death penalty.
"The question of applying the death penalty to the marines has long been totally excluded, both in past statements by Indian Foreign Minister Salman Khurshid," and more recent comments made by the minister, said Italian envoy to India Staffan De Mistura.