"We hope for a rapid, positive solution," Renzi told Modi during a telephonic conversation, ANSA quoted Renzi's office as saying.
Indian Prime Minister Narendra Modi told Renzi that the matter is subjudice and that the country's judicial process should be allowed to take its own course, Xinhua reported.
During the conversation that took place at Italy's request, Modi emphasised that "a fair and early resolution" of the marines issue was in mutual interest of the two countries, an Indian government statement said Monday.
Renzi requested for early resolution of the issue, it added.
Massimiliano Latorre and Salvatore Girone were arrested for killing the fishermen off the coast of Kerala in February 2012, mistaking their fishing boat for a pirate vessel. The two are currently on bail.
Modi encouraged the Italian side to allow the judicial process to take its own course.
In May, the Italian government announced it was opening a "new phase" in the saga, replacing its special envoy in the case and sending its ambassador back to New Delhi to help steer the case towards arbitration.
Italy has long attempted to win international support in the case.
The Indian Supreme Court had March 27 sought a response from the government on the petition filed by the two marines challenging the jurisdiction of NIA to probe and prosecute the case.