The justices voted 5-4 to leave in effect a provision requiring doctors who perform abortions in clinics to have admitting privileges at a nearby hospital.
The court's conservative majority refused the plea of Planned Parenthood and several Texas abortion clinics to overturn a preliminary federal appeals court ruling that allowed the provision to take effect.
The four liberal justices dissented.
The case remains on appeal to the 5th U.S. Circuit Court of Appeals in New Orleans. That court is expected to hear arguments in January, and the law will remain in effect at least until then.
Justice Stephen Breyer, writing for the liberal justices, said he expects the issue to return to the Supreme Court once the appeals court issues its final ruling.
The Texas Legislature approved the requirement for admitting privileges in July.
In late October, days before the provision was to take effect, a trial judge blocked it, saying it probably is unconstitutional because it puts a "substantial obstacle" in front of a woman wanting an abortion.
But a three-judge appellate panel moved quickly to overrule the judge. The appeals court said the law was in line with Supreme Court rulings that have allowed for abortion restrictions so long as they do not impose an "undue burden" on a woman's ability to obtain an abortion. Writing for the appeals court, Judge Priscilla Owen noted that the Texas law would not end the procedure, only force women to drive a greater distance to obtain one.
Justice Antonin Scalia, writing in support of the high court order Tuesday, said the clinics could not overcome a heavy legal burden against overruling the appeals court. The justices may not do so "unless that court clearly and demonstrably erred," Scalia said in an opinion that was joined by Justices Samuel Alito and Clarence Thomas.
Chief Justice John Roberts and Justice Anthony Kennedy did not write separately or join any opinion Tuesday, but because it takes five votes to overturn the appellate ruling, it is clear that they voted with their conservative colleagues.
Planned Parenthood and several Texas abortion clinics said in their lawsuit to stop the measure that it would force more than a third of clinics in the state to stop providing abortions. After the appeals court allowed the law to take effect, the groups said that their prediction had come to pass.
In their plea to the Supreme Court, they said that "in just the few short days since the injunction was lifted, over one-third of the facilities providing abortions in Texas have been forced to stop providing that care and others have been forced to drastically reduce the number of patients to whom they are able to provide care. Already, appointments are being canceled and women seeking abortions are being turned away."
Breyer said the better course would have been to block the admitting privileges requirement at least until the court issued its final ruling because some women will be unable to obtain abortions. If courts ultimately find the law is invalid, "the harms to the individual women whose rights it restricts while it remains in effect will be permanent," he said.
The five justices and three appeals court judges who sided with Texas are all Republican appointees. The four dissenting justices are Democratic appointees. U.S. District Judge Lee Yeakel, who initially blocked the provision, is a Republican appointee.
Texas Gov. Rick Perry, a Republican, praised the Supreme Court action. "This is good news both for the unborn and for the women of Texas, who are now better protected from shoddy abortion providers operating in dangerous conditions. As always, Texas will continue doing everything we can to protect the culture of life in our state," Perry said.
Cecile Richards, president of Planned Parenthood Federation of America, said the groups will continue the legal fight:
"We will take every step we can to protect the health of Texas women. This law is blocking women in Texas from getting a safe and legal medical procedure that has been their constitutionally protected right for 40 years. This is outrageous and unacceptable - and also demonstrates why we need stronger federal protections for women's health. Your rights and your ability to make your own medical decisions should not depend on your ZIP code," Richards said.
Tennessee and Utah are the other states enforcing their laws on admitting privileges. Similar laws are under temporary court injunctions in Alabama, Kansas, Mississippi, North Dakota and Wisconsin.
In Texas, 12 abortion providers say they have attempted to obtain hospital privileges for their doctors, but so far none of the hospitals have responded to the requests. That means those clinics can no longer offer abortions, leaving at most 20 facilities open in a state of 26 million people. All of those facilities are in metropolitan areas, with none in the Rio Grande Valley along the border with Mexico. Currently, only six out of 32 abortions clinics in Texas qualify as ambulatory surgical centers, and some have doctors who do not meet the admitting privileges requirement.
Texas women undergo an average of 80,000 abortions a year.