WASHINGTON — The Supreme Court on Monday reaffirmed and strengthened constitutional protections for abortion rights, striking down parts of a restrictive Texas law that could have drastically reduced the number of abortion clinics in the state, leaving them only in the largest metropolitan areas.

The 5-to-3 decision was the court’s most sweeping statement on abortion since Planned Parenthood v. Casey in 1992, which reaffirmed the constitutional right to abortion established in 1973 in Roe v. Wade. It found that Texas’ restrictions, requiring doctors to have admitting privileges at nearby hospitals and clinics to meet the standards of ambulatory surgical centers, violated Casey’s prohibition on placing an “undue burden” on the ability to obtain an abortion.

If Casey limited the right established in Roe, allowing states to regulate abortion in ways Roe had barred, Monday’s decision effectively expanded that right. It means that similar requirements in other states are most likely also unconstitutional, and it imperils many other kinds of restrictions on abortion. It is also sure to energize anti-abortion forces and make abortion a central issue in the presidential campaign.

The decision concerned two parts of a law that imposed strict requirements on abortion providers in Texas signed into law in July 2013 by Rick Perry, the governor at the time.

One required all clinics in the state to meet the standards for ambulatory surgical centers, including regulations concerning buildings, equipment and staffing. The other required doctors performing abortions to have admitting privileges at a nearby hospital.

“We conclude,” Justice Stephen G. Breyer wrote for the majority, “that neither of these provisions offers medical benefits sufficient to justify the burdens upon access that each imposes. Each places a substantial obstacle in the path of women seeking a previability abortion, each constitutes an undue burden on abortion access, and each violates the federal Constitution.”

Justices Anthony M. Kennedy, Ruth Bader Ginsburg, Sonia Sotomayor and Elena Kagan joined the majority opinion. Chief Justice John G. Roberts Jr. and Justices Clarence Thomas and Samuel A. Alito Jr. dissented.

Justice Kennedy’s vote was the crucial one, and it came as a relief to abortion rights groups, which have long viewed his thinking on the issue as a contradictory muddle.

In the Casey decision, he joined Justices Sandra Day O’Connor and David H. Souter in a joint opinion that reaffirmed the core of Roe v. wade. But Justice Kennedy’s reputation as an abortion rights champion had otherwise been undeserved, said David S. Cohen, a law professor at Drexel University, as Casey was the only case in which he had found an abortion restriction unconstitutional in his 28 years on the Supreme Court.

Professor Cohen said Justice Kennedy’s vote in Monday’s case was a puzzle. He may have been swayed by the burdens placed on women having to drive hundreds of miles to obtain abortions, Professor Cohen said, or by the lack of medical evidence justifying the restrictions — or both.

Many states have enacted restrictions in recent years that test the limits of the constitutional right to abortion, and the ruling in the new case, Whole Woman’s Health v. Hellerstedt, No. 15-274, enunciated principles that will apply to all of the ones said to be justified by a concern for women’s health.

In a message posted on Twitter, President Obama said he was “pleased to see the Supreme Court reaffirm” that “every woman has a constitutional right to make her own reproductive choices.”

Ken Paxton, Texas’ attorney general, said, “The court is becoming a default medical board for the nation, with no deference being given to state law.”

The Texas law was passed in 2013 by the Republican-dominated Texas Legislature and turned a Democratic state senator, Wendy Davis, who conducted an 11-hour filibuster against the law, into a national political star.

Last June, the United States Court of Appeals for the Fifth Circuit, in New Orleans, largely upheld the contested provisions of the Texas law, saying it had to accept lawmakers’ assertions about the health benefits of abortion restrictions. The appeals court ruled that the law, with minor exceptions, did not place an undue burden on the right to abortion.

Justice Breyer said the appeals court’s approach was at odds with the proper application of the undue-burden standard. The Casey decision, he said, “requires that courts consider the burdens a law imposes on abortion access together with the benefits those laws confer.”

In dissent, Justice Thomas said the majority opinion “reimagines the undue-burden standard,” creating a “benefits-and-burdens balancing test.” He said courts should resolve conflicting positions by deferring to legislatures.

“Today’s opinion,” Justice Thomas wrote, “does resemble Casey in one respect: After disregarding significant aspects of the court’s prior jurisprudence, the majority applies the undue-burden standard in a way that will surely mystify lower courts for years to come.”

The majority opinion considered whether the claimed benefits of the restrictions outweighed the burdens they placed on a constitutional right. Justice Breyer wrote that there was no evidence that the admitting-privileges requirement “would have helped even one woman obtain better treatment.”

At the same time, he wrote, there was good evidence that the admitting-privileges requirement caused the number of abortion clinics in Texas to drop from 40 to 20.

In a second dissent, Justice Alito, joined by Chief Justice Roberts and Justice Thomas, said the causal link between the law and the closings was unproven. Withdrawal of state funds, a decline in the demand for abortions and doctors’ retirements may have played a role, Justice Alito wrote.

Justice Breyer wrote that the requirement that abortion clinics meet the demanding and elaborate standards for ambulatory surgical centers also did more harm than good.

“Abortions taking place in an abortion facility are safe — indeed, safer than numerous procedures that take place outside hospitals and to which Texas does not apply its surgical-center requirements,” he wrote, reviewing the evidence. “Nationwide, childbirth is 14 times more likely than abortion to result in death, but Texas law allows a midwife to oversee childbirth in the patient’s own home.”

In dissent, Justice Alito said there was good reason to think that the restrictions were meant to protect women. “The law was one of many enacted by states in the wake of the Kermit Gosnell scandal, in which a physician who ran an abortion clinic in Philadelphia was convicted for the first degree murder of three infants who were born alive and for the manslaughter of a patient,” he wrote.

Justice Breyer acknowledged that “Gosnell’s behavior was terribly wrong.”

“But,” he added, “there is no reason to believe that an extra layer of regulation would have affected that behavior.”

The clinics challenging the law said it had already caused about half the state’s 41 abortion clinics to close. If the contested provisions had taken full effect, they said, the number of clinics would again be cut in half.

The Supreme Court’s decision rippled through the presidential campaign, with Democrats and Republicans looking to rally voters with reminders that the future of the court is at stake.

The next president will have at least one and potentially several vacancies to fill, and Hillary Clinton and Donald J. Trump have both warned that the fate of laws on immigration, guns and abortion will most likely be determined by who gets to fill those openings.

Mrs. Clinton, the presumptive Democratic nominee, seized on the court’s ruling to warn that Mr. Trump, her Republican opponent, poses a threat to women. She recalled his suggestion this year that abortion should be banned and that women who violate that ban should be penalized. She also said that with other states also seeking to restrict access to abortions and with Republicans seeking to defund Planned Parenthood, proponents of abortions rights could not afford to let up.

“We’ve seen a concerted, persistent attack on women’s health and rights at the federal level,” Mrs. Clinton said in a statement. “Meanwhile, Donald Trump has said women should be punished for having abortions.”

Mr. Trump has since retracted his assertion that women should be punished for having abortions, but the re-emergence of the issue is likely to put him on the defensive because of his previous support of abortion rights.

Mr. Trump made no direct public comments on Monday’s decision.

Still, for many Republicans, the decision added urgency to their desire to keep Mrs. Clinton from winning the presidency.

“Today’s disappointing decision is another reminder of what’s at stake in this election and why we can’t afford to let Hillary Clinton win,” Reince Priebus, the chairman of the Republican National Committee, said.

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