Mr. Trump made his decision after months of internal debate over whether to pursue diplomacy or support Israel in seeking to set back Iran’s ability to build a bomb, at a time when Iran has been weakened militarily and economically.

The debate highlighted fault lines between historically hawkish American cabinet officials and other aides more skeptical that a military assault on Iran could destroy the country’s nuclear ambitions and avoid a larger war. It resulted in a rough consensus, for now, against military action, with Iran signaling a willingness to negotiate.