Even as top executives at Facebook and Twitter attempted to fend off questions from senators about election interference on their platforms, Attorney General Jeff Sessions said he plans to gather state attorneys general this month to examine what the Justice Department called the intentional “stifling” of voices on social media.

The department announced the plan as Facebook Inc. Chief Operating Officer Sheryl Sandberg and Twitter Inc. Chief Executive Jack Dorsey were wrapping up testimony Wednesday morning on efforts to deter...