WASHINGTON, July 1 -Justice Sandra Day O'Connor, the first woman to serve on the United States Supreme Court, announced today that she is resigning, setting off what is expected to be a tumultuous fight over confirming her successor.

Justice O'Connor, 75, is widely viewed as the critical swing vote on abortion, affirmative action and other hot-button issues that have divided the court, and her departure is sure to ignite a passionate ideological battle throughout the summer.

Her departure, which had been the subject of rumors for weeks but was still a surprise, will give President Bush his first opportunity to name a justice to the Supreme Court. The retirement of Justice O'Connor creates the first vacancy on the tribunal in 11 years, ending the longest period without a change in the lineup of justices in almost two centuries.

It is still not clear whether Chief Justice William H. Rehnquist, who is battling thyroid cancer and had been widely expected to resign, will step down this summer, giving Mr. Bush another seat to fill.

Chief Justice Rehnquist has been the subject of months of speculation, while talk of Justice O'Connor's possible departure had been much quieter. But it was clear that her announcement was not a total shock: the Senate majority leader, Bill Frist of Tennessee, read a tribute to her on the Senate floor minutes after the announcement, and it was clear that his statement had been prepared.

In a letter sent this morning to the White House, Justice O'Connor said she would step down as soon as her successor was named.

"It has been a great privilege, indeed, to have served as a member of the court for 24 terms. I will leave it with enormous respect for the integrity of the court and its role under our constitutional structure," she said in the three-sentence letter.

Her decision even took allies of the White House by surprise.

"An O'Connor resignation was not one we took seriously," said C. Boyden Gray, a former White House counsel who founded the Committee for Justice, one of the key advocacy groups set to back whoever the president nominates.

Mr. Gray received a text message during an interview with The New York Times at his Georgetown home shortly after 9:30 this morning informing him of Justice O'Connor's resignation.

"It makes me nervous," he said. "I'm not sure we are as prepared for an O'Connor vacancy."

One of the liberal groups expected to be active in the looming confirmation battle, People for the American Way, said the choice of her successor would mark a critical moment. "Justice O'Connor has been the most important figure on the court in recent years," said Ralph G. Neas, president of the group. "Her replacement will have a monumental impact on the lives and freedoms of Americans for decades to come."

Mr. Neas urged the president to engage in bipartisan consultations with the Senate before settling on a nominee and to reject pressure from conservatives for an ideological nominee. Conservatives have never gotten over the Senate's rejection of Robert H. Bork in 1987.