President Bush hailed William H. Rehnquist as one of America's greatest chief justices today as he and other mourners paid tribute to the late jurist during a funeral service attended by Rehnquist's Supreme Court colleagues and a host of national dignitaries.

Bush told the gathering at St. Matthew's Cathedral in Northwest Washington that Rehnquist was a steady steward of the Supreme Court, on which he served for 33 years before his death on Saturday.

"We remember the integrity and the sense of duty that he brought to every task before him," Bush said in his eulogy, the Associated Press reported. He spoke before hundreds of mourners, including Rehnquist family members, former law clerks, members of Congress, high-ranking federal officials and the eight current Supreme Court justices.

In another eulogy, Justice Sandra Day O'Connor, who first met Rehnquist more than 50 years ago at Stanford University law school, recalled her classmate and high court colleague as smart, witty and persuasive.

"He was clearly the brightest student in our class," she said, AP reported. On the Supreme Court, she said, Rehnquist "never twisted arms to get votes," but relied instead on the power of his arguments.

After the two-hour service, the flag-draped wooden coffin bearing the body of Rehnquist was driven to Arlington National Cemetery for a private burial.

At the request of Rehnquist's family, television cameras were barred from the cathedral. Nor was there any live audio coverage.

Upon arrival at St. Matthew's, the casket was carried by eight of Rehnquist's former law clerks past the eight Supreme Court justices who served with him.

Cardinal Theodore McCarrick, the archbishop of Washington, welcomed those attending the funeral and praised Rehnquist as a "loving father and husband, an outstanding legal scholar, a tireless champion of life and a true lover of the law," AP reported. McCarrick said the chief justice was "in every sense, a great American."

Before the funeral, the body of Rehnquist, who died Saturday night at age 80 from thyroid cancer, lay in repose in the Great Hall of the Supreme Court for two days, as thousands of people filed by his coffin to pay their last respects. Among the last to view the coffin there were members of the U.S. Senate, who praised Rehnquist's tenure on the Supreme Court and his handling of the court's business and personalities.

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

Moments before the coffin was removed from the Supreme Court, ministers from the Northern Virginia church Rehnquist attended, the Lutheran Church of the Redeemer in McLean, bowed their heads in prayer. "We thank you for the role that he has played in our lives, his influence among us," said Rev. Jeffrey M. Wilson, associate pastor of the church.

Although Rehnquist was a Lutheran, his family requested that the funeral service be held at St. Matthew's because there was more space in the Roman Catholic church, which seats about 2,000.

Also offering eulogies at St. Matthew's today were two of Rehnquist's children -- James Rehnquist and Nancy Spears -- and his granddaughter, Natalie Lynch.

Rehnquist is entitled to burial at Arlington National Cemetery because of both his position on the Supreme Court and his service in the U.S. Army during World War II. His burial was the last of 29 scheduled today at the cemetery, whose Web site listed him simply as an Army sergeant. "William H. Rehnquist, Sgt., USA," the funeral schedule said.

Rehnquist's wife, Natalie Cornell Rehnquist, who died in 1991 of ovarian cancer at age 62, is buried at Arlington National. The tombstone over her grave also lists her husband's name, with open spaces for the date of his death and the last year of his tenure as chief justice.

President Bush has nominated John G. Roberts Jr., a federal appeals court judge, to replace Rehnquist as chief justice, and Senate confirmations hearings are scheduled to start next week. Roberts was originally named by Bush to replace Justice O'Connor, who announced in July that she would retire upon confirmation of her successor.

After Rehnquist lost his long battle with cancer on Saturday, Bush decided to elevate Roberts to chief justice and choose someone else later to replace O'Connor.