Oct 22 (Reuters) - The U.S. Supreme Court on Friday agreed to hear on Nov. 1 a challenge to a Texas law that imposes a near-total ban on the procedure and lets private citizens enforce it - a case that could dramatically curtail abortion access in the United States if the justices endorse the measure's unique design.

The justices took up requests by President Joe Biden's administration and abortion providers to immediately review their challenges to the law. The court declined to act on the Justice Department's request to immediately block enforcement of the measure.

The court will consider whether the law's unusual design is legally permissible and whether the federal government is even allowed to sue the state to try to block it.

The measure bans abortion after about six weeks of pregnancy, a point when many women do not yet realize they are pregnant. It makes an exception for a documented medical emergency but not for cases of rape or incest.

Liberal Justice Sotomayor dissented from the court's deferral of a decision on whether to block enforcement of the law while the litigation continues. Sotomayor said the law's novel design has suspended nearly all abortions in Texas, the second most populous U.S. state, with about 29 million people.

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"The state's gambit has worked. The impact is catastrophic," Sotomayor wrote.

The Texas dispute is the second major abortion case that the court, which has a 6-3 conservative majority, has scheduled for the coming months, with arguments set for Dec. 1 over the legality of a restrictive Mississippi abortion law.

The Texas and Mississippi measures are among a series of Republican-backed laws passed at the state level limiting abortion rights - coming at a time when abortion opponents are hoping that the Supreme Court will overturn the landmark 1973 Roe v. Wade that legalized the procedure nationwide.

Mississippi has asked the justices to overturn Roe v. Wade, and the Texas attorney general on Thursday signaled that he also would like to see that ruling fall.

Lower courts already have blocked Mississippi's law banning abortions starting at 15 weeks of pregnancy.

The Texas measure takes enforcement out of the hands of state officials, instead enabling private citizens to sue anyone who performs or assists a woman in getting an abortion after cardiac activity is detected in the embryo. That feature has helped shield the law from being immediately blocked as it made it more difficult to directly sue the state.

Individual citizens can be awarded a minimum of $10,000 for bringing successful lawsuits under the law. Critics have said this provision lets people act as anti-abortion bounty hunters, a characterization its proponents reject.

Nancy Northup, president of the Center for Reproductive Rights, which is representing the abortion providers, said Friday's decision to hear their case "brings us one step closer to the restoration of Texans' constitutional rights and an end to the havoc and heartache of this ban."

Northup expressed disappointment that the justices did not immediately block the law.

Kimberlyn Schwartz, a spokesperson for the Texas Right to Life anti-abortion group, praised the court's action, saying it "will continue to save an estimated 100 babies per day, and because the justices will actually discuss whether these lawsuits are valid in the first place."

It is rare that the Supreme Court would, as it did in this case, decide to hear arguments while bypassing lower courts that were already considering the Texas dispute, indicating that the justices have deemed the matter of high public importance and requiring immediate review.

The Justice Department filed its lawsuit in September challenging the Texas law, arguing that it is unconstitutional and explicitly designed to evade judicial review.

The Supreme Court previously allowed the Texas law to be enforced in the challenge brought by abortion providers. In that 5-4 decision on Sept. 1, conservative Chief Justice John Roberts expressed skepticism about how the law is enforced and joined the three liberal justices in dissent.

Rulings in Texas and Mississippi cases are due by the end of next June, but could come sooner.

(Reporting by Andrew Chung in New York; Editing by Will Dunham)