AUSTIN, Texas (AP) — Texas abortion providers who won a landmark U.S. Supreme Court ruling in 2016 that blocked a new wave of anti-abortion efforts are now using that decision to try to undo laws on the books for decades in a lawsuit filed Thursday.

In suing over anti-abortion measures that stretch back 20 years in some cases, Texas clinics are putting a new spin on what has become a recurring cycle in GOP-controlled states — legislatures passing new abortion laws, followed by opponents rushing to court before they can take effect.

Mississippi, which has just one abortion clinic, was similarly...