The 73-year-old was best known for his acting roles in films including "The Hunt for Red October" and on television including a long role in the crime drama "Law & Order."
He served eight years in the US Senate and made a brief bid for the 2008 presidential nomination of the conservative Republican Party.
As a young lawyer, he was a staff member of the US Senate committee investigating then-president Richard Nixon. By some accounts,Thompson had a key role in exposing the Oval Office recording system that led to Nixon's 1974 resignation over the coverup of the Watergate burglary.
Thompson died surrounded by family in Nashville, Tennessee, according to the statement, which was published by the Tennessean newspaper and other US media.