RIYADH, Saudi Arabia—Chinese President Xi Jinping’s arrival here Tuesday kicked off a trip that puts his country at the center of a clash between Saudi Arabia and Iran over crude-oil sales, which are at the core of the regional economy.

China is the largest importer of crude from both Saudi Arabia and Iran, which have long been at odds over such issues as the wars in Syria and Yemen. The recent execution of Shiite clericNemer al-Nemer in Saudi Arabia led to violent protests against the Saudi embassy in Tehran, and Riyadh’s...