Iranian President Hassan Rouhani threatened to revive his country’s nuclear program within hours if the U.S. continues to pile on sanctions, a warning that Iran was prepared to tear up a deal that he championed.

Mr. Rouhani didn’t specify a threshold that would trigger Iran’s departure from the 2015 nuclear deal with six world powers, including the U.S., but, in a fresh escalation of tensions, he said the country could act swiftly if it chose to restart its efforts.

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