The case 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, which on September 1 allowed the law to go into effect, 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 private-enforcement structure prevents federal courts intervening to strike it down 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 realise they are pregnant. It makes an exception for a documented medical emergency but not for cases of rape or incest.

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

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

Mississippi has asked the justices to overturn Roe v Wade, and the Texas attorney-general has signalled he also would like to see it 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.

This has helped shield the law from being blocked as it made it more difficult to directly sue the state.

Australian Associated Press