The US did not want to risk a nuclear confrontation with the communist superpowers.
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The U.S used no nuclear weapons whatsoever on Vietnam.
Fear that the North Vietnamese would obtain nuclear weapons themselves (from Russia or China) and use them on South Vietnam or even on America.
No nuclear weapons were used in the korean war
The United States used the atomic bomb offensively during WWII. That is pretty close to nuclear weapons.
The only country that has ever used nuclear weapons in any war was the US, at the end of WW2.