WASHINGTON — The battle to influence the next Supreme Court pick began Friday as President Barack Obama announced that Justice David Souter would retire at the end of the current term.

Official word of the vacancy came just past 3 p.m. when Mr. Obama literally elbowed aside press secretary Robert Gibbs during a routine briefing. In describing his search for a successor, the president said he would seek a nominee with “a record of excellence and integrity…who understands that justice isn’t about some abstract legal theory or footnote in a case book.”

Mr. Obama also stated his preference for someone attuned to the “daily realities of people’s lives” — a sentiment conservatives have seized upon as a prescription for what they consider to be unwarranted judicial activism.

Over the past three decades, Supreme Court nominations have often turned into pitched ideological battles in the Senate. A big question today is how Mr. Obama will deal with a Republican minority that can delay, but probably not block, any nomination. Democrats and their independent allies control 59 Senate seats; 60 votes are needed to overcome a filibuster.

Democrats fear a prolonged debate over Justice Souter’s successor could crowd out action on other Obama priorities, such as legislation to combat climate change and expand access to health care.

The process for identifying a high court nominee began well before Mr. Obama became president, when a judicial-selection working group was set up in his transition offices to identify candidates for Supreme Court and appellate-court vacancies.

Mr. Obama, a former constitutional-law instructor, suggested names for consideration to the Supreme Court in December during working-group meetings in Chicago and Washington, aides said.

Court observers predicted Mr. Obama would select a woman, and several emerged as contenders. Judge Sonia Sotomayor, who sits on the Second Circuit U.S. Court of Appeals, would be the first Hispanic woman on the court. Two other appellate judges, Kim Wardlaw and Diane Wood, were also mentioned, along with Solicitor General Elena Kagan, a former Harvard Law School dean; Homeland Security Secretary Janet Napolitano, a former federal prosecutor; and Stanford University law Prof. Kathleen Sullivan.

The president said he intends to consult on his choice with Republicans and Democrats across the political spectrum. He said he wants to have a new justice in place by October, when the court’s next term begins.

All the potential candidates being floated are generally viewed as liberal. But Mr. Obama may be more interested in finding someone who can move the law in new directions, either through mastering the court’s internal dynamic to build majorities — as liberal Chief Justice Earl Warren did a half-century ago — or capturing the public imagination with compelling visions of constitutional law, as conservative Justice Antonin Scalia has done since his 1986 appointment.

Liberals, who have been in retreat since Chief Justice Warren retired in 1969, have yearned to see a new champion of progressive jurisprudence pick up the torch. The previous Democratic president, Bill Clinton, chose less controversial nominees — Ruth Bader Ginsburg and Stephen Breyer — who brought legal expertise and intellect but fewer of the political skills possessed by the court’s most effective members.

“President Obama is going to consider more factors than pure ideology,” said Douglas Kendall, president of the Constitutional Accountability Center, a liberal advocacy group.

Mr. Obama can influence the court’s look and sensibility with a second woman or a Hispanic. Even before Justice Souter’s announcement, the Puerto Rican Bar Association started a national campaign for Judge Sotomayor, whom conservative groups have singled out as unacceptably liberal.

Sen. Arlen Specter, the Republican who switched to the Democratic Party this past week, added his voice to those calling for more diversity on the court. “Another female justice would be a good idea,” said Mr. Specter, who sits on the Judiciary Committee. He added that African-American and Hispanic candidates should be considered.

Republicans appeared ready for a fight. Utah Sen. Orrin Hatch, a key Republican player on judicial confirmations, reeled off a series of quotes from Mr. Obama saying a judge should show empathy for the poor and disadvantaged, which Mr. Hatch said meant the judge should tilt the playing field.

“By anybody’s definition, that would be judicial activism,” he said. “Justices on the court should not be for rich or poor, management or labor, or women or men.”

Justice David Souter told the White House he intends to retire, paving the way for President Obama to appoint his first Supreme Court justice. As Fox’s Doug Luzader reports, it could signal a battle ahead. Video courtesy of Fox News.

Sen. Lindsey Graham, another senior Republican on the Judiciary Committee, said Republicans would be “firm and fair” in the process. “If they nominate someone out of the mainstream, that doesn’t go down well with the public,” Mr. Graham said.

Administration officials said Friday that White House Counsel Gregory Craig, who accompanied the president to the press briefing room, would take the lead in the search process. Mr. Craig has already made a show of seeking consensus on court picks, securing Republican Sen. Richard Lugar’s support for his nomination of Indiana Judge David Hamilton for the Seventh U.S. Circuit Court of Appeals in March.

Vice President Joe Biden, a former Senate Judiciary Committee chairman, is a veteran of several Supreme Court battles, including the fierce fights that scuttled Robert Bork and nearly sank Clarence Thomas.

Senate leaders had been looking at June for committee action on health care, with the goal of getting a final vote on legislation in July. Keeping to that timetable could be difficult, if the Senate is at the same time gearing up for a Supreme Court fight.

While delaying the confirmation until September is an option, congressional aides deemed it unlikely, partly because they don’t want to give opponents all summer to plot strategy and comb through the nominee’s background.

—Naftali Bendavid and Greg Hitt contributed to this article.