China’s coronavirus outbreak has sparked fears of a global pandemic—and sent Beijing’s diplomats into overdrive in a bid to keep other countries from adopting measures that imply shortcomings in Chinese efforts to contain the crisis.

While Chinese President Xi Jinping assured foreign counterparts that his government is sparing no effort in a “people’s war” against an epidemic that has killed more than 1,380 people, his foreign minister has worked the phones over the past few weeks, relaying a message of calm and confidence...