The Dow Jones industrial average rose 1.7 percent a few minutes after the open. The broad-based S&P 500 index was up 1.5 percent and the tech-heavy Nasdaq composite index rose 1.6 percent.
Donald Trump wrote earlier in the day that the United States had "very good and productive" talks with Iran about a solution to the conflict.
Shortly afterwards, Iran announced that the parties had not had any discussions, according to Bloomberg, which cited the state-controlled Fars news agency.
