President George W Bush has promised to move quickly to nominate a new chief justice following the death of William Rehnquist on Saturday.
William Rehnquist was known for his conservative views
His death, two months after another top judge said she was retiring, leaves Mr Bush in the rare situation of having two Supreme Court vacancies to fill.
He is likely to face a political battle over his choice of replacements.
Mr Bush paid tribute to Mr Rehnquist, saying his death was "a great loss for our court and for our country".
"There are now two vacancies on the Supreme Court and it will serve the best interest of the nation to fill those vacancies promptly," Mr Bush said.
Mr Rehnquist was a powerful conservative voice in the most powerful court in the US, says the BBC's Jonathan Beale, and Mr Bush will want to replace him with someone like-minded.
He has already nominated a moderate conservative, John Roberts, to replace Sandra Day O'Connor, the Supreme Court judge who announced her retirement earlier this year.
There is some speculation in Washington that the president may now nominate Mr Roberts to the post of chief justice.
Senators are scheduled to scrutinise Mr Roberts' credentials on Tuesday as they decide whether to approve of his nomination.
But the hearings may be delayed to give time to honour Justice Rehnquist and deal with issues surrounding the aftermath of Hurricane Katrina.
Mr Rehnquist's body will lie in repose at the Supreme Court this week.
He died at his Virginia home aged 80, a year after he began treatment for thyroid cancer.
Although he appeared increasingly weak, and had to breathe with the help of a tube at President Bush's inauguration in January, he continued to work.
A frail Rehnquist presided over Bush's January 2005 inauguration
Our correspondent says Mr Rehnquist was politically attuned to Republican politics.
He championed states' rights, supported the death penalty and opposed abortion.
He was nominated to the Supreme Court in 1972, and appointed the nation's 16th chief justice by Ronald Reagan in 1986.
During a remarkable career, he oversaw the court's conservative shift, presided over President Bill Clinton's impeachment hearing in 1999 and helped decide the controversial election of George W Bush as president in 2000.
The nine-seat Supreme Court is one of America's most important institutions and judges are named for life.
Its key responsibilities are to examine laws and government actions to ensure they do not violate the principles laid down in the Constitution.
Its future direction is likely to be the subject of an intense battle in coming months as Democrats fight to stop President Bush giving the two seats to conservatives.