That the talks are even happening represents a historic moment, given the decades of enmity between the two countries since the 1979 Islamic Revolution and the U.S. Embassy hostage crisis.

At risk is a possible American or Israeli military strike on Iran’s nuclear sites, or the Iranians following through on their threats to pursue an atomic weapon.

Mr. Trump’s chief envoy to the talks, Steve Witkoff, has also sent mixed signals over what the United States wants. Over the past week, he has moved from suggesting Iran could have a limited nuclear program to saying Iran needed to fully dismantle it.