The court, on a 5-4 vote along ideological lines Tuesday, said the law's challengers didn't meet the requirement for setting aside a federal appeals court's order that allowed the law to take effect Oct. 31, Scotusblog.com reported.
The law requires any doctor in Texas who performs abortions to have admitting privileges at a hospital within 30 miles of the site where the abortion occurs. Challengers argued that this provision, which carries a fine of up to $4,000 for a violation, was particularly burdensome on pregnant women in the state's rural areas.
"Reasonable minds can perhaps disagree about whether the court of appeals should have granted a stay in this case," Justice Antonin Scalia wrote, joined by Justices Clarence Thomas and Samuel A. Alito Jr. "But there is no doubt that the applicants have not carried their heavy burden of showing that doing so was a clear violation of accepted legal standards -- which do not include a special 'status quo' standard for laws affecting abortion."
Writing for the four dissenting justices, Justice Stephen Breyer said the effect of the law was to leave 24 counties in the Rio Grande Valley without abortion clinics, The New York Times reported.
"It may," he added, "substantially reduce access to safe abortions elsewhere in Texas."
The decision itself was unsigned, but several justices wrote opinions.
Abortion rights groups and clinics said the law fulfilled no medical purpose and was forcing about a dozen of the state's 36 abortion clinics to stop performing the procedure, preventing 20,000 women a year from accessing safe abortions.
State officials countered that the law protects public health by "fostering a woman's ability to seek consultation and treatment for complications directly from her physician."
The law was stalled during its consideration when state Sen. Wendy Davis, a Democrat now running for governor, conducted an 11-hour filibuster in the Republican-controlled Legislature.
The 5th U.S. Circuit Court of Appeals provisionally allowed the law to go into effect last month. The appeals court scheduled arguments in the case in January, and either side may appeal the decision to the Supreme Court.
Breyer wrote the validity of the Texas law "is a difficult question," noting he expected the Supreme Court to agree to hear an appeal regardless of how the appeals court rules.