President Donald Trump on Saturday signaled his chagrin at what he described as China’s inaction on North Korea’s nuclear and ballistic-missile ambitions.

“I am very disappointed in China. Our foolish past leaders have allowed them to make hundreds of billions of dollars a year in trade, yet they do NOTHING for us with North Korea, just talk,” Mr. Trump wrote in a pair of posts on his Twitter account. “We will no longer allow this to continue. China could easily solve this problem!”

On...