WASHINGTON—President Trump moved Thursday to extend tariffs to essentially all Chinese imports, escalating a trade conflict that is poised to hit U.S. consumers in the pocketbook and roiling financial markets.

The new tariffs would take effect Sept. 1 and cover $300 billion in Chinese goods—including smartphones, apparel, toys and other consumer products. They would come on top of tariffs already imposed on $250 billion in imports from China.

“If...