"It is a question of law of the land and we are hoping that courts will find a solution to this problem," Krishna said on the sidelines of a seminar here organised by the Singapore-based Institute of South Asian Studies.
India enjoys the best of relationship with the government of Italy, Krishna said.
Krishna's comments came as Italian Prime Minister held a telephonic conversation with his Indian counterpart Manmohan Singh on the politically sensitive issue.
Jelastine and Ajesh Binki, the two fishermen, were allegedly shot dead by the two Italian marine guards off the Kollam coast on February 15, suspecting them to be pirates.
The marines - Latore Massimiliano and Salvatore Girone - are currently in judicial custody in Kerala following their arrest on February 19.
The state and central authorities had rejected Italy's demand for the case to be tried outside India.
Italian right wing activists have threatened to attack Indian establishments in Italy to protest against the arrest of their nationals in India.