The U.S. government has initiated an extraordinary outreach campaign to foreign allies, trying to persuade wireless and internet providers in these countries to avoid telecommunications equipment from China’s Huawei Technologies Co., according to people familiar with the situation.

American officials have briefed their government counterparts and telecom executives in friendly countries where Huawei equipment is already in wide use, including Germany, Italy and Japan, about what they see as cybersecurity risks, these people...