Facebook Inc. cut references to Russia from a public report in April about manipulation of its platform around the presidential election because of concerns among the company’s lawyers and members of its policy team, according to people familiar with the matter.

The drafting of the report sparked internal debate over how much information to disclose about Russian mischief on Facebook and its efforts to affect U.S. public opinion during the 2016 presidential contest, according to these people. Some at Facebook pushed to not...