The senators emerged from the meeting saying they discussed names of possible nominees with Mr. Bush but would not say who they are, reports CBS News White House Correspondent Mark Knoller.
"He didn't give us any names," Democratic Leader Harry Reid of Nevada said.
Senate Judiciary Chairman Arlen Specter, R-Pa., said he urged Mr. Bush to consider nominating someone who is not currently part of the federal court system.
"It would be good to have some diversity," Specter said. "That was one item which the president listened. The president, of course, speaks for himself, but it was a good meeting and, as already indicated, a good start."
Sen. Patrick Leahy of Vermont, the ranking Democrat on the Judiciary committee, and Senate Majority Leader Bill Frist, R-Tenn., also attended the meeting.
While the president has held telephone conversations with the four before, this was his meeting with them in person on the issue since O'Connor announced her retirement. All four lawmakers said the meeting was a positive step in bipartisan consultation with the White House on whom Mr. Bush will nominate.
"The president was very much in a listening mode," White House press secretary Scott McClellan said.
Laura Bush, meanwhile, said she hoped her husband would pick a woman.
"I would really like him to name another woman," Mrs. Bush said Tuesday on NBC's "Today" show, in an interview from Cape Town, South Africa, where she is traveling. "I admire and respect Sandra Day O'Connor, but I know that my husband will pick somebody who has a lot of integrity and strength."
McClellan would not say whether the president was leaning toward selecting a woman. "The president is going to consider a diverse group of individuals for the vacancy that is available," said McClellan.
Asked about Democrats' objections to specific candidates said to be under consideration, McClellan said, "No individual should have veto power over a president's selection."
Reid said the president indicated that there would be more meetings and consultations.
"He said on several occasions, `If you have anything that you want to bring to my attention, either talk to me or talk or talk to Harriet, Harriet Miers, who is his counsel," Reid said.