The 69-year-old justice, who received sustained standing ovations before and after his 15-minute talk, announced Friday that he will retire when the court finishes its work for the summer and return to New Hampshire.
"It's impossible not to be doing a mental reckoning of some sort," said Souter, who did not permit cameras.
In Washington, the White House said President Obama will not be announcing his choice to replace Souter this week.
Senator Patrick Leahy, chairman of the Judiciary Committee, said he has discussed possible nominees with Obama but would not name potential candidates.
Obama made a brief courtesy phone call yesterday to Senator Jeff Sessions of Alabama, who is now the top Republican on the committee, replacing Senator Arlen Specter, who changed parties last week to join the Democrats. Sessions, in a statement, said he would ensure "a rigorous and thorough examination of his or her qualifications."
He expressed traditional Republican themes on court nominations, saying the nominee must be "a neutral umpire of the law, calling the balls and strikes fairly while avoiding the temptation to make policy or legislate from the bench based on personal political views."
Sessions' ascension comes more than 20 years after the panel rejected him for his own federal judgeship during the Reagan administration over concerns that he was hostile toward civil rights and was racially insensitive.
The choice of Sessions has excited conservatives who see him as a sharp lawyer with well-established legal views after a career as a prosecutor and Alabama attorney general.
Sheldon Goldman, a political scientist at the University of Massachusetts at Amherst, agreed that Sessions has a firm grasp on the issues but said making Sessions "the face of the party" for the Supreme Court nomination might not play well symbolically.
Goldman, who has written a book on judicial nominations, said Specter's defection resulted in part from the perception that the GOP has moved too far right.
"And instead of responding to that by placing a moderate as the ranking Republican, they go for a very conservative Southern Republican who represents everything that has driven Specter and other moderate Republicans out of the party," Goldman said.
Senator Mitch McConnell, Republican of Kentucky, said yesterday that the GOP won't rubber-stamp Obama's choice. "The president is free to nominate whomever he likes," McConnell said. "But picking judges based on his or her perceived sympathy for certain groups or individuals undermines the faith Americans have in our judicial system."
