Chief Justice William H. Rehnquist (search) was buried alongside his wife Wednesday after the nation paid tribute to him in two days of ceremonial mourning.

"It is a rare man who can hold a prominent position in Washington for more than 30 years and leave behind only good feelings and admiration. That's what William Rehnquist did," said President Bush. Rehnquist died on Saturday night at the age of 80.

Hundreds attended the private ceremony honoring Rehnquist, a jurist who was widely admired by those who worked with him and remembered with great affection by those who were close to him. Mourners included the eight Supreme Court justices and John Roberts (search), a former Rehnquist law clerk whom Bush has named to succeed him.

Rehnquist, a veteran of the Army Air Forces in World War II, was buried in a private ceremony in Arlington National Cemetery (search) in a grave not far from those of several other justices. His headstone was not yet engraved. From the grave site, where his wife was buried in 1991, the Capitol is visible.

Bush, speaking at the chief justice's funeral mass at St. Matthew's Cathedral, said while Rehnquist accomplished many things during his 33 years on the nation's highest court, he was also known for being well-liked and respected.

"He carried himself with dignity but without pretense," Bush said. "We remember the integrity and the sense of duty that he brought to every task before him."

Despite battling thyroid cancer, Rehnquist managed to attend Bush's second inauguration in January and administer the oath of office to the president — a gesture Bush recalled with appreciation.

Friends and family talked about his penchant for wagers, jokes, sports, geography, history, tennis, and competition of any type.

"If you valued your money, you would be careful about betting with the chief. He usually won," said Justice Sandra Day O'Connor (search), who dated Rehnquist when both were in law school together in the 1940s. "I think the chief bet he could live out another term despite his illness. He lost that bet, as did all of us, but he won all the prizes for a life well lived."

Comparing Rehnquist to an expert horse rider, O'Connor said, "He guided us with loose reins and used the spurs only rarely." He was, she added, "courageous at the end of his life just as he was throughout his life," even joking with doctors in a final visit to the hospital.

The service, scripted in part by the chief justice before his death, had a light touch. A granddaughter talked about learning poker tips from him. A son said his dad "could forgive almost anything in a person except being humorless."

"No one smelled more roses than my dad," James Rehnquist told the funeral audience.

At the service, Nancy Rehnquist Spears joked about her father's history quizzing and his love of games and gambling. She recalled him promising $5 if she could tell the history buff when Queen Elizabeth died.

"1603," she answered.

"There was silence, then an awful curse," she recalled.

Cardinal Theodore McCarrick, in a welcome to those assembled in the Roman Catholic church, praised Rehnquist as a "loving father and husband, an outstanding legal scholar, a tireless champion of life and a true lover of the law: in every sense, a great American."

Rehnquist's casket was brought to the church from the court, where "The Chief" had lain in repose since Tuesday morning. Heads bowed, the eight remaining justices lined up beside the casket at the court as ministers from the Lutheran Church of the Redeemer, Rehnquist's church in northern Virginia, offered a benediction. "Thank you for the role he has played in our lives, his influence among us," said the Rev. Jeffrey Wilson.

On Tuesday, Roberts was among those who carried the casket into the Great Hall.

Since viewing was opened to the public Tuesday, Americans including dignitaries and admiring citizens have lined up outside the Supreme Court to pay their final respects to the venerated chief.

Defense Secretary Donald Rumsfeld was among Wednesday's visitors. Senators also trickled in from the Capitol across the street to the Supreme Court to honor Rehnquist, who is credited with moving the court to the center and for being an efficient and fair administrator.

"He kept the members of the court together, despite their many differences," said Sen. George Voinovich, R-Ohio.

Pete Domenici, R-N.M., called Rehnquist "a great intellect who matured tremendously" during more than three decades on the court.

The family of Rehnquist, a Lutheran, requested St. Matthew's primarily because of the space the Roman Catholic church provides. The funeral for President Kennedy took place there, and Pope John Paul II celebrated Mass at St. Matthew's in 1979.

The nation's 16th chief justice, who died Saturday night from complications of thyroid cancer, was being buried after the mass at Arlington National Cemetery, where the Web site listed him as William H. Rehnquist, Sgt. USA, a reference to his Army rank during World War II. From the gravesite, where his wife was interred upon her death in 1991, the Capitol is visible.

It has been an emotional two days for Rehnquist's family and his friends, especially his former law clerks, many of whom recalled on Tuesday his devotion to duty and their love for his lack of pretense.

"In some ways, he may be looking down at all of this, and be amused by it all; he was a person who liked being anonymous," said Joseph Hoffmann, a former Rehnquist clerk who teaches law at Indiana University.

"There was a profound love for him," said New York attorney Robert Giuffra Jr., another former Rehnquist clerk. "He was a very approachable, decent person."

Bush initially nominated Roberts, a federal appellate judge and former Rehnquist clerk, to replace O'Connor, who announced in July that she would step down.

The president said Monday that he would nominate Roberts to be the nation's 17th chief justice instead and that the list of possible nominees for O'Connor's seat was now "wide open."

Bush and Senate Republicans are pushing to confirm Roberts before the new court session that begins Oct. 3. Democrats cautioned against a rush to judgment now that Roberts is a candidate for chief justice and at age 50, could shape the court for decades.

Flags, including the one above the court, were at half-staff in honor of Rehnquist, a President Nixon appointee who served on the court for 33 years and was elevated to chief justice in 1986 by President Reagan.

The Associated Press contributed to this report.