In July 2013, the Republican-dominated Texas Legislature passed some of the toughest abortion restrictions in the United States, after a marathon filibuster that turned a Democratic state senator, Wendy Davis, into a national political star and set the stage for her campaign for governor. Some parts of the law were already being enforced, but the surgical-center requirement had yet to take effect.

This August, Judge Lee Yeakel of United States District Court in Austin ruled that the surgical-center rule put an unconstitutional burden on women seeking abortions, and that the effect of clinic closings and the reduced geographic distribution of clinics operated “just as drastically as a complete ban on abortion.” In the months before the law was enacted last summer, Texas had 41 facilities providing abortions. In recent weeks, that number had decreased to 21.

Judge Yeakel also blocked a requirement that doctors performing abortions obtain admitting privileges at a hospital within 30 miles of a clinic.

In an unusual move, the judge granted the abortion providers who sued the state broader relief than they had requested. Lawyers for abortion facilities had asked him to strike down the requirement as it applied to two clinics, in El Paso and McAllen. But Judge Yeakel ruled the admitting-privileges requirement and the surgical-center standards, operating together, put undue burdens on women statewide, and created “a brutally effective system of abortion regulation that reduces access to abortion clinics.”

Lawyers for Mr. Abbott appealed Judge Yeakel’s ruling to the Fifth Circuit, asking the court to temporarily block the decision while the appeal proceeded.

The Fifth Circuit, regarded by many as one of the most conservative federal appellate courts, had given Texas favorable rulings in past abortion cases and was expected to do the same this time. In March, a different Fifth Circuit panel sided with Texas in the first lawsuit over the new abortion restrictions, overturning a decision by Judge Yeakel and upholding the admitting-privileges rule as constitutional.

In court documents and at a hearing in New Orleans, lawyers for Texas had attacked Judge Yeakel’s decision on several fronts, and some of their arguments influenced the circuit panel’s ruling. Jonathan F. Mitchell, the state’s solicitor general, said Judge Yeakel was legally barred from ruling on the statewide impact and constitutionality of the admitting-privileges requirement because the Fifth Circuit had already upheld it in March.