The threats included delivery of a package containing a bullet tied to the case of two Italian marines on trial in India for allegedly killing two Indian fishermen two years ago, Italian news agency ANSA reported.
"We have asked Italian authorities to ensure the protection of diplomatic staff," Syed Akbaruddin, an Indian government spokesman, said. "We are sure our Italian friends will guarantee the safety of our diplomats."
An Indian newspaper reported Thursday the package containing a bullet was sent to the Indian Embassy this week. The newspaper said an anonymous letter contained threats on the marines' case.
Prime Minister-designate Matteo Renzi was reported considering "new initiatives" Wednesday after Italy recalled its ambassador to India over matter, ANSA said. The two anti-piracy marines have been held for two years without charge.
Italian envoys to the United Nations also have raised the issue, sources told ANSA.
Officials and the families of marines Salvatore Girone and Massimiliano Latorre expressed frustration this week when India's Supreme Court announced the latest in a series of delays in the case.
The two men are accused of killing two fishermen in February 2012 after allegedly mistaking them for pirates and firing on their fishing trawler. Girone and Latorre were guarding the privately owned, Italian-flagged oil tanker MT Enrica Lexie off the coast of India's Kerala region at the time.