Muirfield is being urged to look again at its membership rules after voting against allowing women to join the club, losing the right to host golf's Open Championship in the process.

The East Lothian club held a ballot at the end of a two-year consultation on membership but failed to get the two-thirds majority of its 648 eligible voters required to change policy.

Of the 616 members who voted, 397, or 64%, voted in favour of admitting women, while 219, or 36%, voted against.

Golf governing body The R&A said it will not stage The Open at a course that does not admit women as members.

The vote was greeted with anger both in and out of the game, with First Minister Nicola Sturgeon describing the result as "indefensible" and Prime Minister David Cameron saying it was "outdated."

Ms Sturgeon said: "We live in a country where women inhabit the offices of First Minister, the leaders of opposition parties, where we have a woman Lord Justice Clerk, one of our most senior judges (Lady Dorrian), a woman law officer (Solicitor General Lesley Thomson) and women lead businesses the length and breadth of this country.

"The majority of members actually voted in favour of admitting women, which is encouraging, but I sincerely hope those who didn't now reconsider and that the club as a whole revisits the issue."

Mr Cameron told LBC radio: "My general rule is that sports clubs should be totally open to both sexes, and it's outdated not to do that, particularly if you think that you're up to hosting important championships."

Politicians from all parties backed the call for the club - which is owned and run by The Honourable Company of Edinburgh Golfers - to review the decision.

Scottish Liberal Democrat leader Willie Rennie said: "I think any golf club which chooses to discriminate on grounds of gender in 2016 needs to take a long, hard look in the mirror."

Some Muirfield members reportedly had concerns over "slow play" and future changes to club rules if women joined Muirfield.

The Equality and Human Rights Commission said the decision could cost the Scottish economy £100 million.

Muirfield, which last hosted the prestigious competition in 2013, will now be removed from The Open rota but could be considered in future if it changes its policy on female membership.

Martin Slumbers, chief executive of The R&A, said: "The Open is one of the world's great sporting events and, going forward, we will not stage the Championship at a venue that does not admit women as members.

"Given the schedule for staging The Open, it would be some years before Muirfield would have been considered to host the Championship again."

Scottish professional golfer Heather MacRae tweeted: "The 1st time I played Muirfield I had to sit outside after the game as I wasn't allowed in. I sat and watched a member go in with his dog!"

Troon is now the only remaining club on the Open rota to have a male-only membership policy but the South Ayrshire club considers itself a "special case" as it shares facilities with the Ladies Golf Club, Troon.

Both clubs will shoulder the responsibility of hosting this year's Open via a joint Championship committee and a ''comprehensive review'' of membership policy is to be carried out by the end of the year.

Muirfield club captain Henry Fairweather announced the results of the members ballot at the clubhouse in Gullane on Thursday.

He said: ' "Women will continue to be welcome at Muirfield on the course and in the clubhouse as guests and visitors, as they have been for many years.''

The captain said he was "disappointed" with the result of the vote and pointed out members can propose change to the rules of the club at any time.

The Honourable Company of Edinburgh Golfers was founded in 1744 and is said to be the oldest recorded golf club in the world.

It set down the original rules of golf in 1744 and has hosted The Open 16 times.

East Lothian politicians believe the decision will damage the area.

MP George Kerevan said: "The negative impact on the reputation of East Lothian cannot be overstated and it certainly threatens the ability of the county to attract major golfing events in the future.

"I urge the club to continue internal discussions and hold a second ballot."