PORT MORESBY, Papua New Guinea—Vice President Mike Pence and Chinese President Xi Jinping presented conflicting visions for trade and security in the Asia-Pacific, as the U.S. and China vie for global influence.

At a meeting of Pacific Rim leaders Saturday, China’s leader invoked the dark lessons of World War II to warn against conflicts and unilateralism, while Mr. Pence attacked China’s Belt and Road infrastructure initiative for saddling smaller nations with unsustainable debt.