Mumbai, June 12 -- U.S. stocks rallied to their best day in two months, and oil prices fell Thursday after President Donald Trump called off his threat to bomb Iran in the evening. That raised hopes for a potential deal that could get the global flow of oil going again.

The S&P 500 jumped 1.8%, coming off a back-to-back drop that had yanked it back to where it was in early May. The Dow Jones Industrial Average leaped 929 points, or 1.9%, and the Nasdaq composite rallied 2.5%.

Stocks jumped midday after Trump posted that talks with Iran's leadership had reached the highest level and that a signing announcement was imminent. Hopes for a deal that could reopen the Strait of Hormuz pushed oil prices down sharply, with U.S. crude falling 2.6...