BEIJING—Chinese public-health officials urged calm on Sunday even as they warned that the dangerous new virus at the heart of a fast-spreading outbreak is growing more contagious, piling more pressure on an already strained containment effort.

“We are now in a critical period of prevention and control,” Ma Xiaowei, head of China’s cabinet-level National Health Commission, said at a news briefing in Beijing on Sunday to deal with the unnamed coronavirus that has infected more than 2,000 people and killed at least 56, the vast…

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