CLEVELAND — President Trump kept China in his sights on Saturday, using a visit to the industrial Midwest to promote his hard-line trade tactics, while the White House rebuked the Chinese government for demanding that foreign airlines change how they refer to Taiwan.

“We’re going to have to rework trade with China,” he said to an enthusiastic crowd of about 600 in a theater here. “It can’t go on like that.”

Mr. Trump noted that a high-level trade delegation had just returned from meetings in Beijing, and that the administration would consider the next steps in what has become an increasingly bitter confrontation over steel tariffs and China’s theft of American intellectual property.

Just before he spoke, the White House issued a statement sharply criticizing the Chinese government for requiring United Airlines, American Airlines and other foreign carriers to refer to Taiwan, Hong Kong and Macau as part of China on their websites and in other materials.