"I will say the same thing that every president has said since this issue came up, which is I don't have litmus tests around any of these issues," he said at the White House before a bipartisan meeting with senators on the high court nomination.
But he said he is "somebody who believes that women should have the ability to make often very difficult decisions about their own bodies and issues of reproduction."
"I want somebody who is going to be interpreting our Constitution in a way that takes into account individual rights, and that includes women's rights. ... I think part of what our core constitutional values promote is the notion that individuals are protected in their privacy and their bodily integrity, and women are not exempt from that."
He stressed his sense of urgency about filling the vacancy.
"As Justice Stevens said, I think it's very important, particularly given the important cases that may be coming before the Supreme Court, that we get this process wrapped up so that a new justice can be seated and staffed, and can work effectively with his or her colleagues in time for the fall session," Obama said.
Obama is meeting Wednesday with Senate Majority Leader Harry Reid, D-Nev., Sen. Minority Leader Mitch McConnell, R-Tenn., Senate Judiciary Chairman Patrick Leahy, D-Vt., and Sen. Jeff Sessions, R-Ala., ranking Republican member of the Judiciary Committee.
Obama said he's confident "we can come up with a nominee who will gain the confidence of the Senate and the confidence of the country and the confidence of individuals who look to the court to provide even-handed justice to all Americans."
The meeting comes after Obama spoke by phone this week with potential nominees to fill the high court vacancy left by retiring Justice John Paul Stevens, an administration source told CNN.
Solicitor General Elena Kagan, federal appeals judges Diane Wood, Sidney Thomas and Merrick Garland, Michigan Gov. Jennifer Granholm and Homeland Security Secretary Janet Napolitano have been reported on a short list of 10 potential candidates. But it remained unclear who might be getting the most serious consideration.
Meanwhile, a CNN poll found a majority of Americans said they expect Obama to appoint a liberal to the Supreme Court, but only one in four said they prefer that.