LOUISVILLE, Ky. — Kentucky voters rejected a ballot measure aimed at denying any constitutional protections for abortion, handing a victory to abortion-rights supporters who have seen access to the procedure eroded by Republican lawmakers in the deeply red state.

The outcome of the election that concluded Tuesday highlighted what appeared to be a gap between voter sentiment and the expectations of Kentucky’s GOP-dominated legislature, which imposed a near-total ban on abortions and put the proposed constitutional amendment on the ballot. ...