WASHINGTON—President Trump and Chinese President Xi Jinping will seek to revive troubled U.S.-China trade talks this week, in a test of whether their professed personal chemistry can surmount seemingly intractable differences at the bargaining table.

The meeting is widely viewed as a last-ditch effort to get negotiations back on track before Mr. Trump moves forward with new 25% tariffs on $300 billion in Chinese imports. Businesses in the U.S. warn that would raise prices for consumers, disrupt long-established supply chains...