"I think it will happen for sure," Mrs. Bush said about a woman in the Oval Office.
She made the comment in a CNN interview broadcast on Friday, the day before she leaves for Liberia to attend the inauguration of the first female president in Africa.
"I think it will happen probably in the next few terms of the presidency in the United States," Mrs. Bush said.
Rice has said she has no desire to be president when President Bush's second term expires, but Mrs. Bush said: "I'd love to see her run. She's terrific."
Mrs. Bush leaves Saturday night for Africa where she will visit Ghana and Nigeria to promote education and AIDS treatment after leading the U.S. delegation attending the swearing-in of Liberia's President-elect Ellen Johnson-Sirleaf on Monday in Monrovia.
Rice is part of the delegation, as is one of the president's daughters, Barbara, who worked recently at a pediatric AIDS hospital in South Africa. "She's interested in the policy surrounding AIDS and what we can do in our country and in other countries around the world to really stop AIDS," Mrs. Bush said.
During the 13-minute interview in the Map Room of the White House, Mrs. Bush talked about how she and the president try to comfort the families of fallen U.S. troops by saying that their service in the armed forces is helping to establish a stable democracy in the Middle East.
In another gesture of consolation, Mrs. Bush said that on Thursday she called to offer encouragement to the wife of Supreme Court nominee Samuel Alito, Martha-Ann Bomgardner, who left her husband's testy Senate confirmation hearing in tears, eliciting sympathy from senators of both parties.
"I think it's very important for the Senate to have a very civil and respectful hearing for anyone that has been nominated for the Supreme Court or for the other jobs that require Senate confirmation," Mrs. Bush said.
"But on the other hand, my family has been in politics for a long time and I think you do develop a thick skin. Does it ever not hurt? You know, not really."