WASHINGTON—American factory activity in August expanded at the strongest pace in more than 14 years, despite rising tensions with some of the U.S.’s largest trade partners.

The Institute for Supply Management on Tuesday said its manufacturing index rose to 61.3 in August, the highest level since May 2004, from 58.1 in July. Sales of factory-made products, or new orders, output and employment all grew at a faster pace in August.

Tuesday’s...