The fate of the court's historic 1973 Roe v Wade decision legalising abortion throughout the United States and its 1992 ruling in Planned Parenthood v Casey, which reaffirmed Roe, probably will not be known until next June.

But after nearly two hours of arguments, all six conservative justices, including three appointed by former president Donald Trump, indicated they would uphold the Mississippi law.

At the very least, such a decision would undermine Roe and Casey, which allow states to regulate but not ban abortion up until the point of viability, at roughly 24 weeks.

And there was also substantial support among the conservative justices for getting rid of Roe and Casey altogether.

Justice Brett Kavanaugh, a Trump appointee, asked a series of questions about whether the court would be better off withdrawing from the abortion debate and letting states decide.

"Why should the court be the arbiter?" Kavanaugh asked. "There'll be different access in Mississippi and New York, Alabama and California,."

Abortion would soon become illegal or severely restricted in roughly half the states if Roe and Casey are overturned, according to the Guttmacher Institute, a research organisation that supports abortion rights.

Legislatures in many Republican-led states are poised for action depending on the Supreme Court's next decision.

The court's three liberal justices said reversing Roe and Casey would significantly damage the court's legitimacy.

"Will this institution survive the stench that this creates in the public perception that the Constitution and its reading are just political acts?" Justice Sonia Sotomayor asked.

Justice Elena Kagan said the abortion decisions are "part of the fabric of women's place in this country".

Among the conservatives, Chief Justice John Roberts appeared most interested in a less sweeping ruling that would uphold the Mississippi law but not explicitly overrule Roe and Casey.

"That may be what they're asking for, but the thing at issue before us today is 15 weeks," Roberts said, alluding to Mississippi's call to overturn the broader cases.

Even upholding the 15-week ban would mean rejecting the decades-old viability line. Abortion rights supporters say that would still in effect overturn Roe and leave no principled line for when abortions might be banned.

Justice Neil Gorsuch, another Trump appointee, suggested the lack of a rigorous alternative might be a reason to overrule Roe and Casey entirely.

Supporters of both sides in the abortion debate protested in front of the court in Washington, DC, waving signs such as "Her Body Her Choice" and "God Hates the Shedding of Innocent Blood".

The case came to a court with a 6-3 conservative majority that has been transformed by the justices named by Trump, who had pledged to appoint justices who oppose abortion rights.

The court had never agreed to hear a case over an abortion ban so early in pregnancy until all three Trump appointees - Justice Amy Coney Barrett, Gorsuch and Kavanaugh - were on board.

A month ago, the justices also heard arguments over a Texas law that has succeeded in getting around the Roe and Casey decisions and banned abortions after about six weeks of pregnancy. The dispute over the Texas law revolves around whether the law can be challenged in federal court, rather than the right to an abortion.

Despite its unusually quick consideration of the issue, the court has yet to rule on the Texas law, and the justices have refused to put the law on hold while the matter is under legal review.

Australian Associated Press