WASHINGTON — I. Lewis Libby Jr. may have to surrender to authorities within weeks after a federal judge refused his request to remain free pending the appeal of his conviction for lying to a grand jury and the FBI during the CIA leak investigation.

U.S. District Judge Reggie Walton ruled that lawyers for the former chief of staff to Vice President Cheney had not sufficiently demonstrated that an appeals court is likely to overturn the jury’s guilty verdict.

Libby’s fate now rests with a federal appeals court and with President Bush, who could decide to issue a pardon or commute Libby’s two-and-a-half-year prison sentence. Mr. Bush has said he does not intend to intervene during the appeals process, but yesterday’s ruling is sure to prompt heightened pressure from conservatives who do not want to see Libby behind bars.

“Scooter Libby still has the right to appeal, and therefore, the president will continue not to intervene in the judicial process,” a White House spokeswoman, Dana Perino, said in a statement. “The president feels terribly for Scooter, his wife, and their young children and all that they’re going through.”

Libby offered no reaction to Judge Walton’s ruling. After the two-hour hearing, he exited through the rear of the courtroom with federal marshals for processing with probation officials. The Bureau of Prisons will now determine where and when Libby will report for incarceration, a process that could take up to two months. Based on the nature of his crimes, he is likely to be sent to a minimum-security facility within 500 miles of his home.

A bureau spokesman, Michael Truman, said yesterday he could not speculate on where Libby will have to report.

The defense is expected to appeal the judge’s ruling immediately in the hopes that an appellate court will allow him to stay out of prison for the duration of the appeals process, which could last more than a year.

A jury in March convicted Libby on four counts of perjury, obstruction of justice, and making false statements during the federal investigation into the leaked identity of a CIA agent, Valerie Plame. He was not charged with the leak itself, nor was anyone else. The judge last week sentenced him to 30 months in prison, a punishment that aligned with what the prosecution had requested.

Judge Walton was in the position yesterday of defending rulings that he had made before and during the trial — rulings that will form the basis for Libby’s appeal. The defense attorneys sought to establish that those decisions involved a “close question,” increasing the likelihood that an appellate court would disagree with Judge Walton and order a new trial. In denying Libby’s request for bail, the judge cited the “overwhelming” evidence against him, saying he concurred with the jury’s verdict. He also stood firmly behind his earlier decisions, rejecting the defense’s suggestion that they could be overturned.

The judge began the hearing by informing the court that since handing down the sentence, he had received “a number of angry, harassing, and mean-spirited” telephone calls and letters, including some “wishing very bad things on me and my family.”

“Obviously, I find that very troubling,” Judge Walton said. But he added, “Those types of things cannot and will not have an impact on my decision.”

He also took issue with some of the defense’s tactics in seeking bail for Libby. A footnote in the opening pages of the defense’s written brief listed several recent high-profile white-collar offenders who had been granted release pending appeal, including Martha Stewart. If Libby’s attorneys thought that “throwing out these names” would sway the decision, they were wrong, Judge Walton said.

In a more severe rebuke, the judge lambasted the defense for submitting an amicus brief signed by 12 prominent legal scholars from across the political spectrum, including Alan Dershowitz of Harvard University and a failed Supreme Court nominee of President Reagan, Robert Bork. “The submission was not something I’d expect from a first-year law student,” the judge said, suggesting the brief was filed to pressure the court.

The legal arguments yesterday offered a preview of the defense’s case for appeal, focusing on three points: that the appointment of the special prosecutor, Patrick Fitzgerald, was unconstitutional; that Judge Walton overly restricted the defense’s ability to argue that Libby’s false statements were attributable to a bad memory, and that the judge erred in barring the testimony of an NBC reporter, Andrea Mitchell.

The hearing centered on the constitutional claim, and a defense attorney hired to lead Libby’s appeal, Lawrence Robbins, emphasized at the outset that his burden of proof was low.

“The only question this morning is, is this close? Is this a close call,” he told the court, insisting that an appeals court could easily differ with Judge Walton’s initial ruling.

He argued that the Justice Department, in assigning Mr. Fitzgerald to investigate the CIA leak case, violated the appointments clause of the Constitution by giving him too much unchecked power. “Mr. Fitzgerald has the broadest delegation of prosecutorial authority of any independent counsel or special counsel that I know of,” Mr. Robbins said.

Mr. Fitzgerald exerted that authority, Mr. Robbins said, pointing to at least one instance in which the prosecutor signed court papers affecting the handling of classified information. Legally, he said, only the attorney general or his most senior deputies had the power to do so.

“I don’t blame Mr. Fitzgerald,” Mr. Robbins said at one point. “He thought he had all this power. And you know what? He probably did. That’s what’s wrong here, not what’s right.”

Speaking essentially in his own defense, Mr. Fitzgerald was dismissive of the defense’s claims. He disputed the notion that he had unlimited authority, saying senior administration officials, including Mr. Bush, were well aware of what he was doing and that he was “fire-able at will.”

Judge Walton sided with Mr. Fitzgerald. He asserted not only that “there was a limitation on his duties” but that “it is my conclusion that the issue is not a close issue.”