Once again, the Federal Reserve helped save the day for investors.

The United States stock market soared in late trading on Wednesday, shrugging off earlier declines in China and Europe. The powerful rally, which came after several days of severe plunges in the world’s major stock markets, was inspired by soothing words from an influential Fed policy maker.

At a news briefing in New York, William C. Dudley, president of the Federal Reserve Bank of New York, said that the recent turmoil in the financial markets was a risk to the United States economy. Crucially, he added that he found the prospect of raising interest rates next month “less compelling.”

Mr. Dudley’s words were manna for investors who had been starved of good news in recent days. On Thursday, stocks in Asia opened broadly higher for the first time since last week, including in Shanghai, where the main index was up more than 2 percent.