WASHINGTON -- William H. Rehnquist was praised Wednesday for steering the Supreme Court with a steady hand as President Bush and former court colleague Sandra Day O'Connor led a national farewell for the 16th chief justice.

After prayers at the high court, Rehnquist's casket was carried down the steps in front of the building where he had served for 33 years. Burial was set for Arlington National Cemetery after funeral services at historic St. Matthew's Cathedral in downtown Washington.

Bush, O'Connor and family members were to speak.

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.

The justices filed out followed by an honor guard and Rehnquist's casket.

"He kept the members of the court together, despite their many differences," said Sen. George Voinovich, R-Ohio, one of many lawmakers saluting the chief justice who died last Saturday at 80.

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

The senators had walked across the street from the Capitol to the Supreme Court's Great Hall where Rehnquist's body lay in repose on Tuesday and Wednesday before the funeral.

Bush and O'Connor were leading final tributes to Rehnquist at the services. The funeral for President Kennedy took place at St. Matthew's in 1963, and Pope John Paul II celebrated Mass there in 1979.

The family of Rehnquist, a Lutheran, requested St. Matthew's primarily because of the space the Roman Catholic church provides. Vice President Dick Cheney was among other government officials attending.

The nation's 16th chief justice was being buried 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.

Rehnquist will be buried in the older section of the cemetery, not far from where former justices Warren Burger, Harry Blackmun and William Brennan, are interred. The gravesite will have a tombstone chosen by the family rather than a government-issued marker, said Lori Calvillo, a public affairs officer at Arlington.

It had been an emotional two days for Rehnquist's family and his friends, including his former law clerks, many of whom recalled 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.

John Roberts, the former Rehnquist clerk named to succeed his old boss, was among the pallbearers carrying the flag-draped casket into the Great Hall on Tuesday. Other pallbearers handled the duty on Wednesday.

Bush initially nominated Roberts, a federal appellate judge, 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.

On Wednesday morning, a line of hundreds of mourners snaked across the court plaza. People laid long-stem red roses and other flowers on the steps leading to the Supreme Court plaza.

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.