The Tulsa clinic is challenging a 2015 state law that bans dilation and evacuation abortions after 14 weeks.
Abortion-rights advocates said the Louisiana law, if put into effect, would leave the state with only one doctor who may perform abortions.
They say hospitals frequently deny admitting privileges to doctors who provide abortions, for reasons ranging from ideological opposition, fear of backlash, or the fact that their patients rarely need emergency care.
The Supreme Court agreed on Friday to take up an abortion case this term, adding an explosive issue to an already robust docket of controversial issues in the middle of the 2020 presidential election.
Like the Texas law that the court previously struck down, the Louisiana law requires any doctor performing an abortion to have admitting privileges at a nearby hospital; it also requires that clinics that provide abortions be, in effect, mini-hospitals, with everything from wide corridors to expensive equipment. And their lawyers pointed to the Supreme Court's ruling in 2016 which, by a 5-3 vote, struck down an identical law from Texas.
The justices on Friday took no action on another abortion-related case concerning the state of Indiana's effort to revive an abortion-related law requiring women to have an ultrasound 18 hours before having an abortion.
Roberts' vote to block the Louisiana law was a rare vote against an abortion restriction in his more than 13 years as chief justice. The Supreme Court struck down a almost identical Texas law that year in the Whole Woman's Health decision, but that was a court that included Anthony Kennedy. And hospitals increasingly are being taken over by religious organizations, meaning they can refuse to grant privileges to doctors who specialize in abortions.
"The Supreme Court announced on Friday that it will hear June Medical Services v. Gee, a case that could well be the vehicle the Court's conservatives use to gut the right to an abortion", the lede says.
"While Ohio does not have an admitting privileges law now, the court's ultimate decision will have a resounding impact across the country", said a statement from Gonidakis that expressed hope the Court will use the case to overturn the 1973 Roe v. Wade decision that legalized abortion nationwide.
"An undue burden exists, and therefore a provision of law is invalid, if its goal or effect is to place substantial obstacles in the path of a woman seeking an abortion before the fetus attains viability", the court wrote in the 1992 ruling.
The Supreme Court upheld a similar Colorado law in 2000, but in 2014 struck down a MA provision that set a fixed 35-foot (10.7-meter) buffer zone outside abortion clinics.
Conservative Chief Justice John Roberts joined the court's four liberals in the majority when it blocked the law from going into effect.
"If the rule of law means anything, it means that the Court can not sit by and watch as the lower court thumbs its nose at Supreme Court precedent and at people's constitutional rights", Jennifer Dalven, director of the ACLU's Reproductive Freedom Project said in a Friday statement.
The high court legalized abortion nationwide in 1973 and reaffirmed it in 1992 in a ruling that disallowed abortion laws that placed an "undue burden" on a woman's ability to obtain an abortion.
The Louisiana law was passed in 2014 but courts have prevented it from taking effect.
Since Kavanaugh joined the court last October, it has sent mixed signals on abortion. In defending the law, the state of Oklahoma contended that women in the second trimester of pregnancy could find an alternative. The court said Friday that it will hear arguments in a case from Louisiana that is almost identical to a Texas case decided by the court three years ago.