The remaining clinics, lawyers for abortion providers said, would be clustered in four metropolitan areas: Austin, Dallas-Fort Worth, Houston and San Antonio. “There would be no licensed abortion facilities west of San Antonio,” the providers’ brief said, “and the only abortion clinic south of San Antonio would have a highly restricted capacity.”

State officials said the law was needed to protect women’s health. Abortion providers said the regulations were expensive, unnecessary and a ruse meant to put many of them out of business.

Abortion providers and advocates for abortion rights praised the Supreme Court’s stay as a kind of temporary victory, saying they were confident the justices would ultimately decide to review the case.

“This case presents a very, very dramatic impact in the type of restrictions on access to abortion clinics that we’ve seen over the past few years,” said Nancy Northup, the president and chief executive of the Center for Reproductive Rights, whose lawyers were part of the legal team representing the clinics that sued the state. “If this case is not taken by the Supreme Court, it’s going to allow a continuation of the closing of clinics by these sneaky, underhanded methods.”

Amy Hagstrom Miller, the chief executive of Whole Woman’s Health, one of the abortion providers that sued Texas over the law, praised the Supreme Court’s move. “We’re relieved that the high court has, once again, prevented anti-choice politicians from pushing safe and affordable abortion care entirely out of reach for Texas women,” Ms. Miller said in a statement.