Texas Gov. Rick Perry, under questioning from voters in recent days, has switched positions on a 2007 executive order he issued mandating the vaccination of all young girls before they enter sixth grade to ward off cervical cancer.

Mr. Perry's order that Texas school girls receive the vaccine, Gardasil, made by Merck & Co., was overturned by the state legislature and never got off the ground. But it still has roiled conservatives and Christian groups for years.

After...