The two Italian marines accused of killing two fishermen off the Indian southern coast last year were being investigated in Italy over the use of their military weapons, local reports said Wednesday.

Italian police questioned Massimiliano Latorre and Salvatore Girone, already under investigation in Rome over the alleged murder, to verify whether they used their weapons and complied with the rules of onboard engagement correctly.

The 13-month diplomatic row between Italy and India, in which Latorre and Girone were charged with shooting dead two Indian fishermen mistaken as pirates from the merchant vessel Enrica Lexie, deepened after Italy decided not to send back the marines after a four-week leave.

The two had been arrested in India but allowed to return to Italy last month in order to vote in the national elections. They had previously been allowed back for the Christmas holidays and went back to India once their permit expired.

But the Italian government said last week that, given the formal establishment of an international dispute between the two states, and also considered that the marines could face a death penalty under the Indian law, they will be kept and tried in Italy.

The decision sparked Indian Supreme Court ruling that Italy's Ambassador to India Daniele Mancini had no "legal immunity" anymore and could not leave India without permission, which Italy said was a violation of the Vienna Convention on Diplomatic Relations.

For its part, India replied that the move to keep the marines in Italy was itself a violation of international law, with Prime Minister Manmohan Singh calling the situation "unacceptable."

While Italy says that the shooting took place in international waters, India insists the marines should be tried on its soil, where the accident happened.

Italy however still hoped to resolve the dispute on a diplomatic level, saying that it was available to letting an international arbitrator assess the case.