Oil prices tumbled after Trump appeared to back off a military response in Iran, saying he had received assurances that protesters would not be executed.
Asked by an AFP reporter in the Oval Office if US military action was now off the table, Trump replied: "We're going to watch it and see what the process is."
About 20 minutes into trading, the Dow Jones Industrial Average was up 0.4 percent at 49,322.07.
The broad-based S&P 500 climbed 0.5 percent to 6,965.99, while the tech-rich Nasdaq Composite Index advanced 0.7 percent to 23,642.32.
Adam Sarhan of 50 Park Investments described Thursday's early action as a "big relief rally."
Strong results from Taiwan Semiconductor Manufacturing Company lifted shares by more than five percent, while Nvidia, Micron, and other US chip companies also gained.
Goldman Sachs rose 1.7 percent, and Morgan Stanley won 3.2 percent after both firms scored higher profits on a surge in merger advisory services.
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