At the close, the Dow Jones Industrial Average had climbed 0.5 percent, while the broad S&P 500 index gained 0.8 percent and the tech-heavy Nasdaq composite index ended up 1.4 percent.
The close followed a start in which the U.S. stock market, like those in Europe and Asia before it, fell sharply after oil prices plunged in the wake of the Iran war.
Late Monday evening, U.S. President Donald Trump announced that the war against Iran, which the U.S. started together with Israel, may be about to end.
"I think the war is pretty much over, by and large. They have no navy, no communications, they have no air force," Trump said in an interview with CBS News.
That pushed Wall Street sharply the other way, while the price of oil fell to about $90 from the day's earlier highs of around $120.
