President Trump revived his trade war threat with more than a dozen countries on Monday, telling them that they would face steep tariffs on their exports as of Aug. 1 unless they agreed to trade deals by then. The president targeted two of America’s closest foreign allies, Japan and South Korea, as well as Malaysia, Indonesia and South Africa.

Mr. Trump also officially extended the timeline for dozens of other countries to agree to deals with the United States or face tariffs, signing an executive order on Monday afternoon delaying the stiff levies that were supposed to snap back on July 9.

Markets dropped as investors assessed the prospect of more trade conflict with some of America’s closest allies and largest trading partners. The S&P 500 ended Monday down 0.8 percent. Other major indexes also fell.

In nearly identical letters to the president of South Korea and the prime minister of Japan, Mr. Trump wrote that the countries would face a 25 percent tax on their exports next month, adding that “we have decided to move forward with you, but only with more balanced, and fair, TRADE.”

“Please understand that the 25 percent number is far less than what is needed to eliminate the trade deficit disparity we have with your country,” he wrote.

A few hours later, the president posted several more letters to social media detailing tariff rates that products from other foreign countries would face: 40 percent for exports from Myanmar and Laos, 30 percent for exports from South Africa and 25 percent for exports from Malaysia. He quickly followed with new tariff rates for Thailand, Bangladesh, Indonesia and other countries.