Justice O'Connor has regularly cast the deciding vote

Ms O'Connor, 75, has often cast the deciding vote on the nine-member court, leading some US commentators to call her the most powerful woman in America.

She is the first Supreme Court justice to retire since 1994, giving George W Bush his first chance to name a judge.

The former Arizona politician was nominated by Ronald Reagan to serve on the court and took up her seat in 1981.

In a statement at the White House, President Bush praised Ms O'Connor as a "discerning and diligent judge", who has earned universal respect.

He said he would consult with senators to find a successor, and said he would be "deliberate and thorough" in his search.

The president's nomination to the court must be approved by the Senate.

The nation deserves - and I will select - a Supreme Court justice that Americans can be proud of

President George W Bush

Possible successors Watch Bush's tribute

The president called for a "dignified process", which he aims to conclude by the start of the new Supreme Court term in early October.

'Privilege'

Despite originally joining the justices as a conservative, Ms O'Connor became a centrist who regularly voted for both liberal and conservative measures.

Ms O'Connor saw her appointment as a breakthrough for women

The BBC's Justin Webb in Washington says a more reliable conservative could give the court a harder edge on social issues, which would affect the nature of American society for decades.

In a three-sentence letter of resignation to Mr Bush, Ms O'Connor described her 24-term tenure on the court as "a great privilege".

"This is to inform you of my decision to retire from my position as an associate justice of the Supreme Court of the United States, effective upon the nomination and confirmation of my successor," she wrote.

"I will leave it with enormous respect for the integrity of the court and its role under our constitutional structure."

Ruth Bader Ginsburg is currently the only other woman sitting on the bench.

Partisan battle

Liberal and conservative interest groups have been preparing for battle over the appointment of a new justice for many years.

I am confident that President Bush will appoint a Supreme Court Justice who shares his conservative philosophy

Senator John McCain

The departure of Ms O'Connor, whose vote was often crucial, is expected to add greater urgency to the nomination debate.

Senator John McCain, a potential Republic candidate to succeed Mr Bush as president, said of Ms O'Connor: "She did make history."

"I am confident that President Bush will appoint a Supreme Court justice who shares his philosophy, which is a conservative philosophy," Mr McCain told CNN.

According to reports, both camps have amassed record sums to spend on adverts promoting or attacking candidates for the vacancy.

Brian McCabe, president of the conservative pressure group Progress for America, said Mr Bush's choice "deserves genuine consideration - not instant attacks".

Ralph Neas, of the liberal organisation People for the American Way, described the nomination process as "a crucial test" for Mr Bush.