"I thanked the US and the US government for the support that they've given us in this phase of the international discussion," Renzi told a joint press conference after talks with US President Barack Obama.
The new Italian premier said he had also asked to be able to count on Obama for "further support" in the case, which dates back to 2012 and has been hit by a series of legal delays.
"We want the issue to be dealt with at an ever more international level," Renzi added.
As tensions have boiled, Italy last month recalled its ambassador to India and summoned the Indian ambassador to express concern at the delays in the court proceedings.
Marines Massimiliano Latorre and Salvatore Girone are accused of shooting the fishermen off the coast of Kerala while they were serving as security guards on an Italian-flagged cargo ship.
The pair, who have been given bail and are staying at the Italian embassy in Delhi, say they mistook the fishing boat for a pirate vessel and only fired warning shots.
In late February, India dropped plans to prosecute them under tough anti-piracy laws, but prosecutors are now re-examining what charges to bring, which could include murder.
Italy insists the pair should be tried on home soil since the shootings involved an Italian-flagged vessel in what Rome insists were international waters. India asserts the killings took place in waters under its jurisdiction.
The United States for its part has had strained relations with India in recent months over the US justice department's visa fraud case against Indian diplomat Devyani Khobragade over her employment of a domestic servant.