White House press secretary Jay Carney said Obama's "personal opinion is that women should be admitted" to the golf club. Carney said it was "up to the club to decide" but Obama told him he personally thinks women should be welcome.
"We're kind of long past the time when women should be excluded from anything," Carney said.
Republican presidential candidate Mitt Romney, Obama's likely challenger in the autumn election, said "of course" he would allow women in "if I could run Augusta."
"Of course. I am not a member of Augusta. I don't know if I would qualify. My golf game is not that good," Romney said at a campaign stop in Pennsylvania. "If I could run Augusta, which isn't likely to happen, of course I'd have women."
One of the club's longtime sponsors, IBM, has a new female CEO, Virginia Rometty. The last four CEOs at IBM, all male, have been invited to be members. Should IBM fight for women to become members? Is that what shareholders want?
Club chairman Billy Payne said this week it will decide for itself whom to allow in its ranks.
The golf writer for the New York Times told a website Thursday she wouldn't want to cover the Masters again until Augusta National invites a woman to be a member.
"If it were left to me, which it seldom is in the power structure of writer versus editor, I'd probably not come cover this event again until there is a woman member," Karen Crouse told GOLF.com. "More and more, the lack of a woman member is just a blue elephant in the room."
Contacted by The Associated Press, New York Times sports editor Joe Sexton said the comments were, "completely inappropriate and she has been spoken to."
Crouse declined further comment.
Questions about membership were raised at Augusta National chairman Billy Payne's annual news conference Wednesday — the day before the Masters began. Crouse, who became the Times' golf writer last year, attended the briefing, along with more than 100 reporters. Though he was asked repeatedly about women being admitted, Payne maintained it was a club matter and declined to discuss it.
Crouse asked Payne what he would say to his granddaughters about the club not having women as members. Payne said it was a question that deals with membership and declined to answer. She followed up by saying it was a "kitchen-table question, a personal question." Payne responded: "Well, my conversations with my granddaughters are also private."
In a column published Thursday in the Times, Crouse criticized Augusta National, saying the club "founded in 1933 on the bedrock of segregation is obviously not so easily rebuilt — or even touched." Crouse wrote that she was the only woman at the news conference to ask a question and that she held her hand up for 20 minutes before she was called on.