The law, which was to take effect Wednesday, would require clinics to adhere to strict new physical standards and the doctors who perform abortions to have admitting privileges at local hospitals.
The court granted the reprieve after abortion rights groups requested an emergency stay, having unsuccessfully sought to have the law overturned. The stay will probably remain in place at least through the summer while the parties assemble a legal case and the court decides whether to take it up in the next term.
The court did not offer a reason for its 5-to-4 decision, and the law’s ultimate fate remains unclear. The court’s reliably conservative justices — Antonin Scalia, Clarence Thomas, Samuel A. Alito and Chief Justice John G. Roberts Jr. — dissented and would have let the law take effect.