WASHINGTON » The Supreme Court today set the stage for its most important pronouncement on abortion in two decades, agreeing to hear a dispute over efforts by some conservative states to regulate the procedure.

The justices accepted an appeal from abortion-rights advocates who are challenging a Texas law that imposed new medical regulations that would in effective shut down three-fourths of the state’s clinics that perform abortions.

The decision is likely to be handed down in June, just as the presidential campaign moves into high gear.

Under a 2-year-old law that has not been fully enforced, Texas clinics that perform abortions must meet the standards of an outpatient surgical center and have doctors who are granted admitting privileges at a nearby hospital.

At issue is whether these are reasonable regulations designed to protect the health of women or costly and unnecessary rules adopted to close down as many abortion facilities as possible.

In 1992, the high court said states may regulate abortion as long as they do not put an “undue burden” on women seeking to end a pregnancy. But since then, justices have not defined exactly what that means.

In recent years, Republican-led states have adopted a series of stringent medical regulations that apply only to abortion facilities. Lower courts have split over whether these laws violate the right to abortion set in the Roe vs. Wade decision of 1973.

The new case before the high court, Whole Woman’s Health vs. Cole, poses two major questions, one medical and one legal.

The medical question is whether the Texas regulations would “raise the standard of care and ensure the health and safety of all abortion patients,” as the state’s lawyer has said.

Abortion-rights advocates maintain that the regulations “will jeopardize women’s health by drastically reducing access to safe and legal abortion services throughout the state.” Outside the state’s five major cities — Houston, Dallas, Fort Worth, Austin and San Antonio — women will not have an abortion facility within easy driving distance, they said.

About 17 percent of the women in the huge state “would face travel distances of 150 miles or more,” the 5th U.S. Circuit Court of Appeals said in upholding the regulations.

Women in the west Texas town of Lubbock would face a 300-mile one-way drive to reach an abortion clinic if the law goes into effect, abortion-rights lawyers said Friday.

Four major medical groups, including the American Medical Association and the American College of Obstetricians and Gynecologists, filed a brief telling the high court that the Texas regulations “do nothing to protect the health and safety of women.” Early abortions rarely result in complications, they said.

“From 2009 through 2013 (when the new law was adopted), there were zero reported deaths in 360,059 abortions performed in Texas,” the medical groups reported. They noted that other “generally riskier” medical procedures are not regulated as stringently. “For example, no law requires colonoscopies or liposuction to be performed in an ambulatory surgical center or hospital, and the mortality of both procedures is higher than abortion,” they said.

The legal question concerns the standard for deciding whether state abortion regulations are constitutional.

The 5th Circuit Court in New Orleans said judges should not “second guess” legislatures and must uphold a disputed law as long as it is “rationally related to a legitimate state interest. … Medical uncertainty underlying a statute is for resolution by legislatures, not the courts.”

In their appeal, lawyers for the Center for Reproductive Rights said that standard would render the right to abortion a “hollow protection” for pregnant women. They said the state should have to show some evidence its regulations would improve the health of women and would not put a “substantial obstacle” before women seeking an abortion.

They also noted that the 7th Circuit Court in Chicago had blocked a Wisconsin law that was similar to the Texas measure.

“Today the Supreme Court took an important step toward restoring the constitutional rights of millions of women, which Texas politicians have spent years dismantling through deceptive laws and regulatory red tape,” said Nancy Northup, president of the center. “We are confident the court will recognize that these laws are a sham and stop these political attacks on women’s rights, dignity, and access to safe, legal essential health care.”

The announcement Friday was no surprise, because the justices intervened in June to block the Texas law from taking effect. But the court’s order came on a 5-4 vote, with Chief Justice John G. Roberts and Justices Antonin Scalia, Clarence Thomas and Samuel A. Alito dissenting.

Abortion is perhaps the most divisive controversy the justices face, and the upcoming case will again put the spotlight on Justice Anthony M. Kennedy.

A moderate conservative appointed by President Ronald Reagan in 1988, he was expected at first to join with fellow conservatives such as Justice Antonin Scalia in voting to overturn Roe vs. Wade.

But in 1992, he surprised many, including his colleagues, when he cast the crucial fifth vote to preserve the right to abortion in a case called Planned Parenthood vs. Casey. He joined with Justices Sandra Day O’Connor and David Souter in writing a compromise opinion that allowed states to regulate — but not to prohibit — abortion. Two other Republican appointees —Justices John Paul Stevens and Harry Blackmun — joined with them to form the majority.

Now, Kennedy is the only justice left who signed the 1992 opinion.

In the court’s only significant abortion cases since then, Kennedy joined with the court’s conservatives to uphold the laws against so-called “partial-birth abortions,” which occur late in a pregnancy.

Defenders of the Texas law now under scrutiny describe it as the kind of reasonable regulation that Kennedy and the court called for 1992. Texas Attorney General Ken Paxton said in the statement that the “common sense measures” will “ensure Texas women are not subject to substandard conditions at abortion facilities. The advancement of the abortionindustry’s bottom line shouldn’t take precedent over women’s health.”

Melissa Conway, a Houston-based spokeswoman for Texas Right to Life, said abortion facilities “are not being forced to close. They’re choosing not to stay open because they do not want to invest the money in improving conditions.”

Texas had at least 40 abortion providers when the law was passed. Currently, 18 remain open, and if the law takes full effect, only nine would remain open in a state with 5.5 million women of reproductive age, abortion-rights lawyers said.

Heather Busby, executive director of NARAL Pro-Choice Texas, said the impact of the facility closings would fall on low-income women. “If you get pregnant and you’re poor and you can’t miss work, what are you going to do” if the nearest clinic is more than 250 miles away, she asked. “We’re creating a reproductive health system where only those who have money and the connections to access it will still be able to.”

Mississippi has a similar law on the books that would force the closure of the state’s only remaining licensed abortion clinic. But federal judges have blocked the law from taking effect, and the high court has yet to act on a pending appeal from the state. That case probably will be held until the Texas case is decided.

The court told the lawyers it probably will hear arguments in the case early in March.