NEW DELHI—India’s government blasted Facebook Inc.-owned messaging service WhatsApp following a series of deadly attacks on victims mistakenly accused of kidnapping children, after rumors and false reports of trafficking activities circulated on the messaging platform.

India’s Ministry of Electronics and Information Technology said in a written statement late Tuesday that it warned WhatsApp—based in Menlo Park, Calif.—about the rumors and false information on the messaging platform in India and has directed its senior management...