The case now returns to Federal District Court in Washington, where Judge Thomas F. Hogan will hear arguments on Wednesday about when and where the reporters, Judith Miller of The New York Times and Matthew Cooper of Time magazine, will begin to serve their time.
Ms. Miller has said she will go to jail rather than testify. "Journalists simply cannot do their jobs without being able to commit to sources that they won't be identified," she said in a statement yesterday. "Such protection is critical to the free flow of information in a democracy."
Representatives for Mr. Cooper were less categorical, saying they would file a motion to reargue the case and make no final decision until Judge Hogan ruled on it.
The one-line order by the Supreme Court yesterday was the resolution of the gravest confrontation between the press and the government in a generation, and it came at a time when the news media are under growing pressure and scrutiny over issues of accuracy, credibility and political bias.
The case arose after the identity of a covert C.I.A. officer was disclosed not by the two reporters facing jail but by Robert Novak in a syndicated column two years ago. The federal appeals court in Washington ruled in February that the reporters must testify because they might have first-hand evidence of a federal crime.
A special prosecutor, Patrick J. Fitzgerald, is investigating whether people in the administration broke a law meant to protect intelligence agents when they told reporters about the officer, Valerie Plame. Several senior administration officials have testified before a grand jury.
In recent months, Mr. Fitzgerald has focused solely on Ms. Miller and Mr. Cooper. Mr. Cooper wrote about Ms. Plame only after the Novak column had identified her, and Ms. Miller, though she conducted interviews on the subject, has never written about it.
Mr. Novak's role in the investigation, including whether he has cooperated with the authorities, remains a mystery. His lawyer, James Hamilton, declined to comment yesterday.
With the Supreme Court's decision not to hear the case, it appears that the first and perhaps only people who will serve time as a result of the inquiry had no part in the conversations that prompted it.
Mr. Fitzgerald indicated yesterday that he would seek to have the reporters jailed immediately.
"Now that the legal obligations of the reporters are settled and all appeals exhausted," he said in a statement, "we look forward to resuming our progress in this investigation and bringing it to a prompt conclusion."
In October, Judge Hogan held the reporters and Time Inc. in civil contempt. He ordered the reporters to testify or else be jailed for 18 months or "the life of the term of the grand jury." It is unclear how soon the grand jury investigation may end. The judge also ordered Time Inc. to turn over documents concerning the case or pay $1,000 a day.
In a statement issued yesterday, Time Inc. left open the possibility that the company or Mr. Cooper might yet comply with the order.
"We think it premature for Time Inc. and Matt Cooper to articulate final positions until Judge Hogan has ruled on our request for review and reassessment," the statement said.
Mr. Cooper's personal lawyer, Richard A. Sauber, said in an interview, "I think everything is up in the air at this point." Theodore J. Boutrous Jr., a lawyer for Time and Mr. Cooper, declined to elaborate on Time's statement for publication.
Experts in law and journalism differed about the obligations of reporters to comply with final court orders in cases involving confidential sources. Some said that refusing to comply was necessary to uphold the promises reporters made to their sources and that it amounted to a form of civil disobedience. Others said reporters were not above the law.
In 1971, The New York Times said that it would abide by the final decision of the courts considering whether it could continue to publish a classified history of the Vietnam War known as the Pentagon Papers. In that case, the Supreme Court upheld the paper's position.
The Pentagon Papers case and the current one differ, the publisher of The Times, Arthur Sulzberger Jr., said in an e-mail interview, in that Ms. Miller is honor-bound to keep her promise.
"Ultimately," Mr. Sulzberger said, "it was Judy's decision to disclose or not to disclose the names of her confidential sources. She made an initial promise to her sources that she would not divulge their names and, subsequently, made a moral decision to keep her promise. In the Pentagon Papers situation, the decision involved no such agreements to others and therefore, abiding by the decision of the court did not mean breaking our word or that of a reporter."
Geoffrey R. Stone, a law professor at the University of Chicago, said that going to jail in the face of a lawful court order amounted to "irresponsible martyrdom."
"If the press wants the public to respect its rights," Mr. Stone said, "it must respect the rights of others. That means, in this case, providing evidence to the grand jury."
Yesterday's decision means that the reporters have largely run out of legal road. In their motion for re-argument, lawyers for Time said they would rely in part on a disclosure that Mr. Fitzgerald made in court filings in the spring and repeated yesterday.
"By October 2004," Mr. Fitzgerald said in his statement yesterday, "the factual investigation - other than the testimony from these reporters and any further investigation that might result - was for all practical purposes completed."
In its statement, Time Inc. said the landscape had changed enough in the meantime to warrant re-argument.
"There is reason to believe, for example, that the special counsel may have determined that disclosure of Valerie Plame's identity to Robert Novak did not violate the Intelligence Identities Protection Act," the statement said, adding that Mr. Fitzgerald might now be investigating a perjury or obstruction of justice charge.
Lawyers for several officials who appeared before the grand jury said that judging from the questions posed by the prosecutor, Mr. Fitzgerald appeared to be exploring whether there was a concerted plan at the White House to leak Ms. Plame's identity as a means of discrediting her husband, Joseph C. Wilson IV, a former diplomat.
Mr. Wilson was the author of an Op-Ed article critical of a rationale offered by the administration to justify the war in Iraq that was published in The Times eight days before the Novak column. Mr. Wilson based his criticism on a trip he took for the C.I.A. to Africa. Mr. Novak's column suggested that the trip was a boondoggle arranged by his wife.
In an interview yesterday, Mr. Wilson said the imminent jailing of the reporters "is a direct result of the president refusing to hold his own administration accountable." He also said the reporters' sources "have acted cravenly."
Mr. Bush has long urged officials to cooperate with the investigation.
In his October decision, Judge Hogan ordered the reporters to be "confined at a suitable place" while they served their time for contempt. On Wednesday, in addition to Time's motion to reargue the case, Judge Hogan is likely to hear suggestions about where that place should be.
The federal regulations governing civil contempt suggest that the local jail, in the District of Columbia, is the default facility. The United States Marshals Service, which has primary responsibility for supervising people held in civil contempt in federal cases, may choose another facility "due to medical, security or other reasons," the federal regulations say. Judge Hogan is also free to specify a different place.
Lawyers for the reporters are likely to propose home confinement or a federal facility other than the District of Columbia jail.
