The Supreme Court seemed poised on Wednesday to uphold a Mississippi law that bans abortions after 15 weeks of pregnancy, in what would be a momentous and polarizing decision to roll back the abortion rights the court has defined over the last half century.

During sometimes tense and heated questioning in almost two hours of oral arguments, the court’s six conservative justices signaled they are comfortable with the Mississippi law, even though upholding it would be flatly at odds with Roe v. Wade, the 1973 decision that established a constitutional right to abortion and prohibited states from banning the procedure before fetal viability, currently around 23 weeks.

Moving that line to 15 weeks would discard decades of precedent. Several of the conservative justices appeared ready to go further and overrule Roe entirely, letting states decide whether and when to ban abortions — an outcome that would transform regulation of abortion in 20 or more states that have been seeking to impose more restrictions and that would further inflame the long-running political and cultural divisions over the issue.

“You’re arguing that the Constitution is silent and, therefore, neutral on the question of abortion?” Justice Brett M. Kavanaugh asked a lawyer for Mississippi, with seeming approval. “In other words, that the Constitution is neither pro-life nor pro-choice on the question of abortion but leaves the issue for the people of the states or perhaps Congress to resolve in the democratic process?”

Until the last few years, the prospect of overruling Roe would have seemed far-fetched. But President Donald J. Trump came into office having vowed to name justices who would overrule Roe. His three appointees have reshaped the court, which now has a six-justice conservative supermajority.

The court’s three liberal members said that overruling Roe soon after a change in the court’s membership would damage the court’s legitimacy. Indeed, Justice Sonia Sotomayor said, doing so would pose an existential threat to the court.

“Will this institution survive the stench that this creates in the public perception that the Constitution and its reading are just political acts?” she asked.

“If people actually believe that it’s all political, how will we survive?” she asked. “How will the court survive?”

The most significant change in the court’s composition was the most recent one. Justice Ruth Bader Ginsburg, who died last year, was a committed supporter of abortion rights, saying that access to the procedure was crucial to women’s equality. Her replacement, Justice Amy Coney Barrett, is a conservative who has spoken out against “abortion on demand.”

Emboldened by the changes, state legislatures have enacted scores of restrictions and bans, many of them at odds with existing precedent, in the hopes of winning a favorable outcome from the Supreme Court in cases like the one heard by the justices on Wednesday.

The law at issue in the case, Dobbs v. Jackson Women’s Health Organization, No. 19-1392, was enacted in 2018 by the Republican-dominated Mississippi Legislature. It banned abortions if “the probable gestational age of the unborn human” was determined to be more than 15 weeks. The statute, a calculated challenge to Roe, included narrow exceptions for medical emergencies or “a severe fetal abnormality.”

Chief Justice John G. Roberts Jr., who is both an institutionalist and an incrementalist, proposed taking a significant step that would stop short of allowing states to bar abortion entirely.

“The thing that is at issue before us today is 15 weeks,” he said, suggesting that the court could uphold Mississippi’s law and leave for another day the question of whether earlier cutoffs are constitutional.

“If you think that the issue is one of choice, that women should have a choice to terminate their pregnancy, that supposes that there is a point at which they’ve had the fair choice — opportunity to choose — and why would 15 weeks be an inappropriate line?” he asked.

But none of the other conservative justices gave much indication that they were interested in the chief justice’s intermediate approach.

Justices Samuel A. Alito Jr. and Neil M. Gorsuch asked a series of questions of the lawyer for the Jackson Women’s Health Organization, Mississippi’s sole abortion clinic, suggesting that they saw no half measures.

The arguments were a vivid display of the continued intensity of the divide over abortion and the issues it touches on. The justices and advocates on both sides debated topics that ranged from the weight that should be given to the court’s precedents to the fundamental rights of women and what it means to have life.

The court’s decision is not expected until June or July, and coalitions at the court may shift as the justices deliberate and exchange draft opinions. But the vote on the bottom line of whether the Mississippi law passes constitutional muster, on the evidence of Wednesday’s questioning and the justices’ earlier writings, seemed likely to be 6 to 3, splitting along the usual lines.

The court’s three liberal members — Justices Stephen G. Breyer, Sonia Sotomayor and Elena Kagan — were adamant that Roe should stand, and they will presumably dissent.

The live question in the case is whether Chief Justice Roberts can attract votes from the other conservative justices for his narrower approach, one upholding the Mississippi law but not overruling Roe in so many words. It seemed that he would face an uphill fight.

Justice Amy Coney Barrett, for instance, asked a question suggesting that a ruling overturning Roe would not have a ripple effect on rulings on the right to privacy or gay rights. She also asked questions about the availability of adoptions.

Still, Chief Justice Roberts worked hard to narrow the question before the court.

When it decided Roe in 1973, the court said states could not ban abortions before fetal viability, the point at which the fetus can survive outside the womb. That was around 28 weeks at the time, but because of improvements in medical technology, it is around 22 to 24 weeks now.

Roe also established a framework to govern abortion regulation based on the trimesters of pregnancy. In the first trimester, it allowed almost no regulations. In the second, it allowed regulations to protect women’s health. In the third, it allowed states to ban abortions so long as exceptions were made to protect the life and health of the mother.

The court discarded the trimester framework in 1992 in another landmark decision, Planned Parenthood v. Casey. But Casey retained what it called Roe’s “essential holding” — that women have a constitutional right to terminate their pregnancies until fetal viability.

On Wednesday, Chief Justice Roberts repeatedly questioned whether the viability line — the standard that allows abortions up to 22-24 weeks — was crucial and whether it was an integral part of Roe.

His point, it seemed, was that the court could move the line without overruling Roe.

“Was viability an issue in the case?” he asked Scott G. Stewart, Mississippi’s solicitor general, referring to Roe. “I know it wasn’t briefed or argued.”

Mr. Stewart said no.

The chief justice acknowledged that Casey called viability “the core principle or a central principle in Roe.” But he said that nothing in Casey — which also gave states leeway to impose restrictions on abortions if they did not impose an “undue burden” on women — turned on viability.

Chief Justice Roberts added that much of the rest of the world has limits similar to the one in the Mississippi law.

Julie Rikelman, a lawyer for the abortion clinic challenging the Mississippi law, disputed that, saying that limits in many other countries are subject to significant exceptions.

Should Roe be overturned, at least 20 states will immediately or in short order make almost all abortions unlawful, forcing women who can afford it to travel long distances to obtain the procedure.

In remarks to reporters on Wednesday, President Biden said the court should leave its abortion jurisprudence undisturbed. “I support Roe v. Wade,” he said. “I think it’s the rational position to take and I continue to support it.”

At the argument, Mr. Stewart, Mississippi’s lawyer, said that Roe and Casey have caused turmoil and should be overruled outright. The decisions, he said, “haunt our country.”

“They have no basis in the Constitution,” he said. “They have no home in our history or traditions. They’ve damaged the democratic process. They’ve poisoned the law. They’ve choked off compromise.”

Mr. Stewart said the availability of abortion is a question best determined by the political process, not judges.

“Abortion is a hard issue,” he said. “It demands the best from all of us, not a judgment by just a few of us.”

Chief Justice Roberts expressed frustration with Mississippi’s litigation strategy. In the state’s petition seeking Supreme Court review, officials told the justices that “the questions presented in this petition do not require the court to overturn Roe or Casey,” though lawyers for the state did raise the possibility in a footnote. Once the court agreed to hear the case, the state shifted its emphasis and began a sustained assault on those precedents.

That amounted to a bait-and-switch, Chief Justice Roberts suggested.

Mr. Stewart said the state was presenting the court with all of the available options.

Ms. Rikelman, representing the abortion clinic, urged the justices to respect precedent and women’s autonomy.

“For a state to take control of a woman’s body and demand that she go through pregnancy and childbirth, with all the physical risks and life-altering consequences that brings, is a fundamental deprivation of her liberty,” Ms. Rikelman said. “Preserving a woman’s right to make this decision until viability protects her liberty while logically balancing the other interests at stake.”

The more liberal justices pressed Mr. Stewart on the dangers of overruling a longstanding precedent after changes in the membership of the court.

Justice Breyer quoted from Casey: “To overrule under fire in the absence of the most compelling reason to re-examine a watershed decision would subvert the court’s legitimacy beyond any serious question.”

He said the court’s authority was at stake.

“Feelings run high,” he said. “And it is particularly important to show what we do in overturning a case is grounded in principle and not social pressure, not political pressure.”

Justice Kagan said that the court should not unsettle a half-century of law under Roe and Casey.

“Some people think those decisions made the right balance and some people thought they made the wrong balance,” she said. “But in the end, we are in the same exact place as we were then — except that we’re not, because there’s been years of water under the bridge, 50 years of decisions saying that this is part of our law, that this is part of the fabric of women’s existence in this country.”

But Justice Kavanaugh said that some precedents deserved to be overruled.

“If you think about some of the most important cases, the most consequential cases in this court’s history, there’s a string of them where the cases overruled precedent,” he said, listing several, notably Brown v. Board of Education, which barred segregation in public schools.

“Why then doesn’t the history of this court’s practice with respect to those cases tell us that the right answer is actually a return to the position of neutrality?” he asked.