Chandy made it clear that the crime was committed in the Indian waters and the two marines must face the Indian law.
"Our stand is very clear, very open...The two soldiers of Italy committed a crime within the purview of Indian law..... They have to face this trial. That is our stand," he told PTI.
His statement came at a time when Italy has been building pressure on the Centre as well as the state government for transfer of the two marines to their home country for trial.
Italian Defence Minister Giam Paolo di Paolo met Chandy three days back to press this issue.
Marines Latore Massimiliano and Salvatore Gironi, on board vessel `Enrica Lexie`, were arrested for allegedly gunning down the two fishermen of Kerala on February 15.
Italian counsel has approached Kerala High Court seeking quashing of the FIR against the marines. Chandy underlined that the Indian judiciary is "very fair, very open and very independent" and the accused can seek justice in this country.
Asked what he would do if the Centre tries to influence the state government on the issue on diplomatic ground, the Chief Minister made it clear that he would not change his stand.
He said the central government was extending full support to the state. At the same time, Chandy said Italy is a friendly country and he wanted the diplomatic relations to continue.
Relations between India and Italy have been under stress ever since the arrest of the two marines.