WASHINGTON—President Trump said Monday he will impose new tariffs on about $200 billion in Chinese goods and threatened to add hundreds of billions more as part of his campaign to pressure Beijing to change its commercial practices, escalating trade tensions between the world’s two largest economies.

The 10% tax on Chinese imports will take effect on Sept. 24 and will rise to 25% at the end of the year, according to administration officials. The tariffs will affect thousands of goods ranging from luggage to seafood, extending...