WASHINGTON, June 26 -- Stepping for the first time into the wrenching political and moral debate over doctor-assisted suicide, the Supreme Court ruled today that states may continue to ban the practice but at the same time suggested that the door remained open to constitutional claims for assistance by dying patients in the future.

In a pair of 9-to-0 decisions, the Court rejected constitutional challenges to laws in New York and Washington that made doctor-assisted suicide a crime. But the Court's tone was that of a tentative first step rather than a definitive final ruling on the issue.

In concurring opinions that accounted for a majority of the Court, various Justices suggested that at least some terminally ill people in intractable pain might be able to claim in the future that they had a constitutional right to a doctor's assistance in hastening their deaths.

''Our opinion does not absolutely foreclose such a claim,'' Chief Justice William H. Rehnquist said in the Court's principal opinion, which was signed by four other Justices.

One of those four, Justice Sandra Day O'Connor, said that while she agreed there was ''no generalized right to 'commit suicide,' '' she viewed as still open the question of whether ''a mentally competent person who is experiencing great suffering'' that cannot otherwise be controlled has a constitutionally based ''interest in controlling the circumstances of his or her imminent death.''

The decisions came amid a torrent of other rulings from the Court in the final week of its 1996-97 term, in which the Justices also invalidated a Federal law banning indecent speech on the Internet and dismissed a challenge to the line-item veto, the President's power to kill individual items of spending in bills that he signs into law.

The session is now expected to end on Friday with a ruling in a states' rights challenge to the Brady gun control law.

The inconclusive nature of the ruling on doctor-assisted suicide was perhaps the most surprising aspect of a decision that was widely seen, in its bottom line, as a foregone conclusion. The Court was never likely to embrace the expansive views of due process or equal protection taken by the two Federal appeals courts whose decisions were reversed today. The lower courts had declared New York's and Washington's criminal prohibitions against assisted suicide to be unconstitutional.

Throughout the opinions today, the Court's tone was measured and sober, in contrast to the sharp language that sometimes pervades the Court's constitutional debates. The Court seemed to be inviting further developments. Chief Justice Rehnquist noted that ''throughout the nation, Americans are engaged in earnest and profound debate about the morality, legality and practicality of physician-assisted suicide.'' He said the Court's approach ''permits this debate to continue, as it should in a democratic society.''

Although the Court did not address the question directly, there was at least a strong suggestion in Chief Justice Rehnquist's opinion, as well as an explicit discussion in a concurring opinion by Justice David H. Souter, that states were free to experiment and permit doctor-assisted suicide if they chose to do so. The Court should ''stay its hand to allow reasonable legislative consideration,'' Justice Souter said.

Only one state, Oregon, has voted to permit doctor-assisted suicide, in a referendum that has yet to go into effect because of prolonged court challenges. The Justices have been asked by opponents of the measure to hear a challenge to its constitutionality, but that case will not come up for consideration until the Court's next term. Meanwhile, the Oregon Legislature decided to put the question to voters again, in November

One reason for the somewhat inconclusive outcome today was the way in which Chief Justice Rehnquist structured his opinion in the Washington State case, which dealt with the question of whether a right to doctor-assisted suicide should be recognized as an aspect of the ''liberty'' protected by the 14th Amendment's guarantee of due process.

The Chief Justice essentially reframed the question that five doctors had raised when they brought their lawsuit on behalf of three dying patients. The question, as the lower court interpreted it, was whether mentally competent, terminally ill adults had a right to a doctor's assistance in determining the time and manner of their death.

The United States Court of Appeals for the Ninth Circuit, in San Francisco, answered yes in a 1996 opinion that drew on the Court's constitutional precedents on the right to abortion and the right to reject unwanted life-sustaining treatment.

Chief Justice Rehnquist, however, put the question in the case on a higher level of generality: ''Whether the protections of the due process clause include a right to commit suicide with another's assistance.'' The answer to that question was no, he said, given several factors that he said were relevant: a 700-year history of disapproval of suicide and assisted suicide in the Anglo-American legal tradition; ''the considered policy choice of almost every state,'' and strong state interests in protecting vulnerable people and avoiding the ''path to voluntary and perhaps even involuntary euthanasia.''

In their concurring separate opinions other Justices objected to the Chief Justice's formulation of the question. Justice Stephen G. Breyer said the Court should have considered a different way of describing the question, one ''for which our legal tradition may provide greater support.'' He said: ''That formulation would use words roughly like a 'right to die with dignity.' But irrespective of the exact words used, at its core would lie personal control over the manner of death, professional medical assistance, and the avoidance of unnecessary and severe physical suffering -- combined.''

Justice Breyer said there was no need to decide in this case whether a right described in that way was protected by the Constitution because in both New York and Washington, doctors are permitted to prescribe pain-killing drugs, even in potentially lethal doses, so that ''the laws before us do not force a dying person to undergo that kind of pain.''

In a separate opinion, Justice John Paul Stevens said he viewed the decision today as being in much the same posture as the Court's decisions that upheld the death penalty 20 years ago. ''Just as our conclusion that capital punishment is not always unconstitutional did not preclude later decisions holding that it is sometimes impermissibly cruel,'' Justice Stevens said, ''so is it equally clear that a decision upholding a general statutory prohibition of assisted suicide does not mean that every possible application of the statute would be valid.'' He said there were ''situations in which an interest in hastening death is legitimate'' and ''entitled to constitutional protection.''

Justice Stevens said he did not agree with the appeals court that there was a categorical right involved, but said he recognized ''the possibility that an individual plaintiff seeking to hasten her death, or a doctor whose assistance was sought, could prevail in a more particularized challenge.''

It was this assertion that Chief Justice Rehnquist acknowledged in his opinion, at the same time adding that ''such a claim would have to be quite different'' from ones involved in this case. He did not elaborate.

In both the Washington case, Washington v. Glucksberg, No. 96-110, and the New York case, Vacco v. Quill, No. 95-1858, the Chief Justice's opinions for the Court were joined by Justices O'Connor, Antonin Scalia, Anthony M. Kennedy, and Clarence Thomas. In addition to the separate opinions by Justices O'Connor, Stevens, Souter and Breyer, Justice Ruth Bader Ginsburg indicated in a brief statement that she agreed with Justice O'Connor's approach.

In the New York case, which also began as a lawsuit by doctors and terminally ill patients, the United States Court of Appeals for the Second Circuit, in Manhattan, took a different approach to striking down the New York law. The appeals court said that because New York permitted terminally ill patients to hasten their death by ordering withdrawal of life-sustaining medical treatment, the prohibition against doctor-assisted suicide violated the rights of other dying patients who were not dependent on particular equipment or treatment.

In his opinion overturning this decision, Chief Justice Rehnquist said that ''unlike the Court of Appeals, we think the distinction between assisting suicide and withdrawing life-sustaining treatment, a distinction widely recognized and endorsed in the medical profession and in our legal traditions, is both important and logical.'' He added: ''It is certainly rational.''

The Chief Justice was the author of the Court's decision in 1990, in Cruzan v. Missouri Department of Health, that for the first time recognized a right to forgo unwanted treatment. As with the decisions today, the Cruzan decision left important issues unsettled and divisions within the Court unresolved.

The dispute over the Cruzan decision flared up again in a very telling way today in an oblique debate between the Chief Justice, who said the decision was based on little more than the common-law rule that ''forced medication was a battery,'' and Justice Stevens, who interpreted the decision as a much more affirmative recognition of a ''more basic concept of freedom that is even older than the common law.''

Justice Stevens said the right recognized in the 1990 decision, which concerned a young woman being kept alive in a persistent vegetative state, was ''not merely a person's right to refuse a particular kind of unwanted treatment, but also her interest in dignity, and in determining the character of the memories that will survive long after her death.''

Reaction to the rulings today was voluminous, reflecting the intense interest the cases had generated. More than 60 briefs were filed, a near record for the Court. Among those expressing satisfaction with the decision was President Clinton, who opposes assisted suicide and who recently signed into law a prohibition against using any Federal money, including Medicaid money, to pay for doctor-assisted suicide.