The 27th Day (1957)

Starring Gene Barry, Valerie French, George Voskovec, Arnold Moss, Stefan Schnabel
Directed by William Asher
(actor & director credits courtesy IMDB.com)

An alien being gives a doomsday weapon to each of five representatives from the Earth, giving them the option of using or not using it within a 27 day period.

Heavy-handed at times, and perhaps unfair in its casting of the Soviet Union's leaders as villains, although their nation is never specifically named, this picture still offers an interesting morality tale quite relevant at the time- if you were given a weapon that dangerous could you trust turning it over to your government for safe-keeping?  The resolution the film comes to is a bit too much of an easy answer, but it's still an entertaining movie, with a fine roster of quality actors in the cast.