Interviewed by Italian state broadcaster Rai in New Delhi, where they are awaiting trial, riflemen Salvatore Girone and Massimiliano Latorre said they were sorry for the deaths of the two fishermen off southern India in 2012.
"We regret the loss of two human lives, but we do not feel we are responsible at all - we are innocent," said Girone.
"The accusation of terrorism is deeply painful for us, not only as military men but as parents and human beings," added Latorre.
India accuses the marines of shooting dead the two unarmed fishermen off the coast of the southern Indian state of Kerala in February 2012 while guarding an Italian oil tanker during an anti-piracy mission.
The marines claim they believed the unarmed fishermen were pirates and only fired warning shots in the air.
India claims jurisdiction in the case while Italy alleges the incident took place in international waters and top officials including president Giorgio Napolitano and premier Enrico Letta have called for Latorre and Girone's return home.
Earlier on Thursday, Italy's foreign minister Emma Bonino said the marines "are neither terrorists nor pirates".
Her comments came ahead of an expected ruling on Monday by the Indian Supreme Court in New Delhi on a petition by Rome drop the case against Girone and Latorre to return to Italy and avoid prosecution under tough Indian legislation that carries the death penalty.
The pair have been custody in India for almost two years and claim that formal charges have not yet been laid against them.
Last week European Commission president Jose Manuel Barroso warned India the European Union was "very closely following" the case of the two marines and opposed capital punishment "in any situation".
The case has thrown a spotlight recent practice of placing private and military armed guards on ships as protection against pirate attacks.
Maritime experts say it is the first test of whether military personnel enjoy sovereign immunity aboard commercial vessels.