It may have been a made for tv movie, I’m not entirely sure. But I recall sometime during the mid-1970’s seeing a rerun movie where the premise was the US and some small country got into a dispute - not exactly sure why but it may have possibly been a satellite that fell into their territory. In any event, it was decided that rather than fighting a lopsided war with this little country - where the US would come off looking like the Bad Guys in world opinion - each country would instead send their best man to an isolated island where the two would fight it out to the death to determine the winner of the conflict.
During the course of the movie, both countries attempted to cheat by secretly sneaking in an extra man, but both of the original combatants killed off the ‘extras’ sent by their own governments as a matter of honor. I also recall the ending involved the American being the first to kill the other guy, but died from his own wounds moments later.
For the life of me I can’t think of the title, but the movie had a distinctly early-70’s feel to it. It was a two word title “The [something]”