Louisiana officials seeking to prosecute a New York doctor who sent abortion medication to a resident of that state were thrown a roadblock on Thursday, when New York’s governor, Kathy Hochul, said she would block extradition attempts.

Ms. Hochul’s declaration sets the stage for a likely battle in federal court over whether states that support abortion rights can protect doctors who provide abortion services to patients in states with abortion bans.

The Louisiana case is the first criminal indictment to test a key strategy of states that support abortion rights: so-called shield laws, enacted in eight states, stipulating that officials and agencies of those states will not cooperate with legal actions taken by states with abortion bans against out-of-state abortion providers.

The Louisiana extradition order is for Dr. Margaret Daley Carpenter, of New Paltz, N.Y. In January, a Louisiana grand jury issued a criminal indictment against Dr. Carpenter, accusing her of violating Louisiana’s near-total abortion ban by sending pills to a pregnant teenager in that state.

“I will not be signing an extradition order that came from the governor of Louisiana — not now, not ever,” Ms. Hochul said at a news conference on Thursday.

The Louisiana charges followed a separate civil suit filed against Dr. Carpenter in December by the attorney general of Texas, alleging that she had flouted that state’s abortion ban by prescribing and sending pills to a woman there.