BEIJING — For the better part of two decades, China’s leaders have made the most of the global trade rules set by the United States and others, seizing on opportunities to bolster their nation’s economic rise while finessing American complaints that they were not always playing fair.

Now, for the first time, China faces an American president who is embracing protectionist measures, and that has presented its leader, Xi Jinping, with an extraordinary challenge: Even as he has elevated his status as the country’s “helmsman,” with a new mandate to rule indefinitely, the United States is moving to treat China more seriously as a strategic rival and to recast an economic relationship that has long bound the two countries.

The punitive actions unveiled by President Trump on Thursday — tariffs on $60 billion worth of Chinese goods, as well as new restrictions on Chinese investment in the United States — put Mr. Xi on the spot, forcing him to consider retaliatory action.

On Friday, China said it was proposing additional tariffs on 128 American products valued at $3 billion even as it called on Washington to resolve the dispute through negotiations to “avoid damage to the broader picture of Chinese-U.S. cooperation.”