WASHINGTON—An influential group of China experts called for Americans to acknowledge what it described as a growing threat of Beijing-sponsored influence operations in the U.S. The cohort also proposed restricting visas for Chinese media and scholars unless their American counterparts are allowed to operate more freely in China.

In a new report, 32 longtime China watchers warned that the Chinese Communist Party’s efforts to influence U.S. universities, media, think tanks and companies—but haven't included attempted election-meddling—have...