BEIJING—A rare public confrontation between the top U.S. and Chinese diplomats marked a new level in the worsening relations between the world’s two biggest economies and risked complicating an anticipated summit meeting between President Trump and North Korean leader Kim Jong Un.

Secretary of State Mike Pompeo exchanged testy words with Foreign Minister Wang Yi in Beijing on Monday at a critical moment for U.S.-China relations, with trade negotiations stalled, military talks halted and both sides blaming each other for a...