Merck & Co. is helping bankroll efforts to pass state laws requiring girls as young as 11 or 12 to receive the drugmaker’s new vaccine against the sexually transmitted cervical-cancer virus.

Some conservatives and parents’-rights groups say such a requirement would encourage premarital sex and interfere with the way they raise their children, and they say Merck’s push for such laws is underhanded. But the company said its lobbying efforts have been above-board.