Definitely "The Bedford Incident"
The film also featured a very young Donald Sutherland playing, if memory serves, a pharmacist's mate. Who, incidentally, without having recourse to Google, imdb or other internet resources, can name the other high-seas epic from the same period with both Richard Widmark and Sidney Poitier in leading roles? (Does "the mare of steel" ring a—heh,heh—bell?)
cordially,
Die Welt ist alles, was der Fall ist.