Noting that all nine justices came directly from the federal appeals court, senators on the committee said someone with a wider breadth of experience would be a plus.
When he was discussing the qualities he would seek in Souter's successor, Obama said last week he wanted someone with empathy for average Americans. Conservatives fear that means the president would consider "judicial activists" for the seat.
Leahy said he expects the next justice to be confirmed by the court's new term in October and that the president will consult with lawmakers from both parties.
"I would like to see, certainly, more women on the court.
Having only one woman on the Supreme Court does not reflect the makeup of the United States. I think we should have more women. We should have more minorities," Leahy said.
Sen. Arlen Specter of Pennsylvania, a committee member who last week switched from the Republican to the Democratic Party, suggested someone in the mold of a statesman or stateswoman, and said he could imagine a nominee who was not a lawyer, if that a person had the right credentials.
"I would like to see somebody with broader experience," Specter said. "We have a very diverse country. We need more people to express a woman's point of view or a minority point of view, Hispanic or African American ... somebody who's done something more than wear a black robe for most of their lives."
Obama said Friday he would nominate a person who combines "empathy and understanding" with an impeccable legal background "who understands that justice isn't about some abstract legal theory or footnote in a case book. It is also about how our laws affect the daily realities of people's lives."
Utah Sen. Orrin Hatch, a senior Republican on the Judiciary Committee, said he hopes Obama will choose someone of "great dimension." At the same time, he said that Obama's criteria raise concern and he contended that the president says he will select a nominee according to that person's politics, feelings and preferences.
"Those are all code words for an activist judge, who is going to, you know, be partisan on the bench," Hatch said.
"We all know he's going to pick a more liberal justice. Their side will make sure that it's a pro-abortion justice. I don't think anybody has any illusions about that," he said. "The question is, are they qualified? Are they going to be people who will be fair to the rich, the poor, the weak, the strong, the sick, the disabled."
Sen. Richard Shelby, an Alabama Republican who is not on the committee, said empathy should be only part of the criteria for a nominee and that a justice should follow the law, not make it.
"But if he will appoint a pragmatist, someone who is not an ideologue ... I think that would be good for the country," Shelby said.
Although Shelby noted that Obama voted against the two most recent nominees to the court - Chief Justice John Roberts and Justice Samuel Alito, both conservatives picked by President George W. Bush - he said he would not seek "payback" in considering Obama's nominee.
Shelby spoke on CNN's "State of the Union" while Leahy and Hatch appeared on ABC's "This Week." Specter spoke on CBS' "Face the Nation."
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