* Use of law sore point in international dispute
* New Italian PM Renzi says personally following case
* Italians, on bail in India, deny aiming at boat (Adds comment from Italian prime minister)
NEW DELHI, Feb 24 (Reuters) - - India has dropped a plan to prosecute two Italian marines accused of killing two Indian fishermen under a tough anti-piracy law, a government lawyer said on Monday, offering a chance to end a diplomatic row between the two countries.
Italy had strongly opposed India invoking the law, arguing that it would amount to treating the men as terrorists and last week it recalled its ambassador to New Delhi in protest against the delay in the two-year-old case.
The sailors, part of a military security team protecting a privately owned cargo ship, say they mistook the fishermen for pirates and fired warning shots into the water during the incident in February 2012, off the coast of Kerala state.
Indian attorney general Ghoolam Vahanvati told the Supreme Court on Monday the prosecution did not intend to proceed against Massimiliano Latorre and Salvatore Girone under the anti-piracy section of the Suppression of Unlawful Acts. He gave no reason.
"We want to delete the anti-piracy clause," he said. The men can still be tried under India's criminal laws, but the punishment in case of a conviction is ordinarily less stringent than under the piracy law.
Nevertheless, new Italian Prime Minister Matteo Renzi made it clear on Monday that the issue will remain a priority under his government, saying that he had made two "symbolic telephone calls" to the marines as one of his first acts as premier since his Saturday swearing in.
"I chose to call the two marines because for too long they have been stuck in New Delhi in an absurd and infuriating affair for which I guarantee my personal effort and that of the government," Renzi told the Senate in his first parliamentary address.
The dispute over the marines has stoked international tension and the European Union had expressed concerns about the use of the anti-piracy law. There is wide public support for the marines in Italy, while in India, supporters of harsh penalties for the men have marched on the streets.
India had originally sought to prosecute the marines under the piracy law partly because the incident occurred outside the geographical area covered by the country's criminal code.
It said, however, that the sailors would not face the death penalty, which the anti-piracy law usually carries, because it has not permitted the investigation agency handling the case to invoke that particular clause in the legislation.
India's Supreme Court on Monday said it would rule on whether the National Investigation Agency which handles cases relating to national security should investigate the fishermen's deaths at its next hearing. It gave no date for the session.
The top court ruled over a year ago that a trial would take place in India, but charges have not yet been filed. Defence lawyers for Italy and the marines maintain that the incident happened beyond India's jurisdiction.
The delays in filing charges, not unusual in India's notoriously slow legal system, spurred Italy to approach the Supreme Court last month demanding a nod for the marines to return home and a block on any use of the anti-piracy law.
The two men deny killing anyone or aiming directly at the fishing boat. They are on bail but cannot leave India. (Reporting by Suchitra Mohanty, and Naomi O'Leary in Rome; Writing by Sanjeev Miglani; Editing by Ron Popeski and Alison Williams)