* Augusta clings to men's-only membership policy

* Club faces dilemma with IBM's woman CEO

(Adds quotes and background)

WASHINGTON, April 5 (Reuters) - President Barack Obama

believes women should be allowed to join the all-male Augusta

National Golf Club, the White House said on Thursday, adding

pressure on the exclusive 80-year-old organization to drop its

restrictive policy.

"His personal opinion is that women should be admitted,"

White House spokesman Jay Carney told reporters, saying he had

spoken to Obama about the issue, as the prestigious Masters

tournament got under way in Augusta, Georgia.

In a rare moment of agreement with Obama, Republican

front-runner Mitt Romney, the Democratic president's likely

opponent in the Nov. 6 election, said if it were up to him, "of

course I'd have women in Augusta."

The question of whether women should be allowed to become

members at the home of the Masters has been around for years.

But it took on added significance after Ginni Rometty became

chief executive officer of IBM, one the tournament's longtime

sponsors, in January.

The White House weighed in on the issue during an election

campaign in which Obama and his fellow Democrats are seeking to

exploit a "gender gap" in polls showing the president ahead of

Republican presidential contenders with women voters. Obama is

hosting a conference on women and the economy on Friday.

Carney was asked whether Obama believed the men's-only

Augusta club should open its ranks to women, especially given

Rometty's position.

"It is obviously up to the club to decide," Carney said at

the daily White House briefing. "He believes Augusta should

admit women. You know, we're kind of long past the time when

women should be excluded from anything."

Club chairman Billy Payne was pressed on the eve of the

Masters on whether the club would alter its policy.

And in keeping with the club's secretive traditions, he

refused on Wednesday to provide a clear answer, saying only that

membership issues were not for public debate.

DILEMMA WITH IBM

IBM, the world's largest technology services company, is a

long-standing sponsor of the Masters and its past four CEOs have

been granted membership to Augusta National.

The club now faces a dilemma of whether to change its policy

to allow Rometty to join or spurn one of its major sponsors.

Augusta's invitation-only membership has been steeped in

secrecy since the conservative club opened in 1932. Women are

allowed to play the course if invited by a member but cannot

become members themselves. The club resisted pressure to

desegregate for decades and only admitted its first black member

in 1990.

The club does not reveal its full list of members, believed

to be around 300, although it is known that some of the powerful

men from industry and finance, including Bill Gates and Warren

Buffett, are members.

When asked whether Obama - who has played golf regularly

during his presidency - would ever play at a men's-only club,

Carney said, "I didn't have that conversation with him."

Carney pushed back against the notion that Friday's White

House conference on women and the economy had electoral

implications, insisting it was meant to promote economic

initiatives.

But Obama's re-election campaign has made no secret of its

efforts to court women voters, and his fellow Democrats have

sought to depict the Republicans' focus on contraception and

abortion as an attack on women's rights.

At a campaign stop in Pennsylvania, Romney took care not to

give the Democrats any more ammunition.

"I'm not a member of Augusta. I don't know if I would

qualify - my golf game is not that good - but certainly if I

were a member and if I could run Augusta, which isn't likely to

happen, but of course I'd have women in Augusta. Sure," he said.

Women voters have helped Obama take a large lead over

Romney in a dozen battleground states, a USA TODAY/Gallup poll

said on Monday. Obama led among the women surveyed in those

states with 54 percent, compared to Romney's 36 percent.

(Additional reporting by Laura MacInnis and Lily Kuo; Editing

by Frances Kerry and Cynthia Osterman)