The Bedford Incident (1965)

An American news writer assigned to interview the captain of the destroyer USS Bedford bears witness to a stunning game of cat and mouse in the frigid waters of the northern Atlantic. A Soviet submarine has been tailing the Bedford and the captain of the Bedford turns tail to confront the Soviet sub. As the cat-and-mouse pursuit continues, the Bedford's captain becomes more obsessed with the Soviet sub, until an accident involving one of his increasingly shaken crewmen leads to a confrontation no one wants, and that no one can win.