WASHINGTON -- Chief Justice William H. Rehnquist died Saturday evening at his home in suburban Virginia, and President George W. Bush has promised a timely choice for a successor.

Rehnquist was 80. He served on the high court for 33 years.

In a nationally broadcast tribute from the White House Sunday morning, Bush offered the nation's respect and deepest sympathy to "this good man's children." They were at his side when he died.

The president said Rehnquist was respected for his powerful intellect, respect for the rule of law and profound devotion to duty. Bush noted that the chief justice stayed on the job even during his illness to complete the work of his final term.

Bush also said he was "honored and deeply touched" when Rehnquist came to the Capitol last January to swear in Bush for his second term.

Since being diagnosed last October, Rehnquist continued to perform his duties on the court until a precipitous decline in his health the last couple of days, said Supreme Court spokeswoman Kathy Arberg.

Rehnquist will lie in repose in the Great Hall of the Supreme Court on Tuesday and Wednesday.

The public will be able to pay its respects Tuesday from 10:30 a.m. until 10 p.m. EDT, and on Wednesday from 10 a.m. until noon.

Rehnquist will be buried Wednesday at Arlington National Cemetery, where his wife was laid to rest in 1991.

Justice John Paul Stevens, the court's senior justice, will fill the administrative role of chief justice until a new one is confirmed.

Stevens repeatedly clashed with Rehnquist over court rulings, but called him "an inspiration to those of us privileged to serve with him."

Rehnquist was appointed to the Supreme Court as an associate justice in 1971 by President Richard Nixon and took his seat on Jan. 7, 1982. He was elevated to chief justice by President Ronald Reagan in 1986.

Rehnquist's death opens up the chief justice seat on the Supreme Court for the first time in two decades.

The president could elevate a current justice to the top chair, possibly Antonin Scalia or Clarence Thomas. Or he could pick someone new, even the current Supreme Court nominee John Roberts, 50.

Bush picked Roberts, a conservative, white male to replace retiring Justice Sandra Day O'Connor and will undoubtedly face pressure to name a woman or a Hispanic for the additional vacancy.

Without O'Connor, Justice Ruth Bader Ginsburg will be the sole female on the court.

Politics will play a role, too. If Bush wants to put an conservative on the high court, his nominee would have to weather a confirmation brawl in the Senate. Analysts say that with approval ratings the lowest of his presidency, Bush may not be ready for that.

Rehnquist's death ends a remarkable 33-year Supreme Court career during which he oversaw the court's conservative shift, presided over an impeachment trial and helped decide a presidential election.

Rehnquist was born Oct. 1, 1924, in Milwaukee. He was the second-oldest chief justice in U.S. history. The oldest died at age of 87.

He underwent a tracheotomy at Bethesda Naval Hospital in Maryland on Saturday, Oct. 23, 2004.

In 2002, Rehnquist missed some court sessions after falling and hurting his knee. He also struggled with chronic back pain over the years.

Rehnquist cast the deciding vote to stop the ballot recount in the 2000 election. In 1973, he voted against the decision to legalize abortion in Roe v. Wade. He's particularly known for supporting states' rights over the federal government.

Rehnquist married his college sweetheart Natalie Cornell in 1953. They were married for some 38 years when she died in 1991.