Priebke, who was sentenced to life in prison in 1998 for his role in a massacre at Rome's Ardeatine caves in March 1944, spent the last few years under house arrest at his lawyer's Rome apartment.
The media reported that Priebke, who never expressed remorse for the massacre which left 335 people dead, including 75 Jews, had left "a written interview and a video as a human and political will and testament."
The former officer had been arrested in 1994 after fleeing to Argentina at the end of World War II.
He had lived there for more than 40 years before being extradited to Italy in 1995.