* Brotherhood says will not monopolise new coalition
* Group said to control SNC, channel funds to supporters
* Qatar, Turkey have backed Brotherhood in Syria opposition
By Rania El Gamal and Andrew Hammond
DOHA, Nov 13 (Reuters) - Syria's Muslim Brotherhood finally swung behind a new opposition unity deal in Qatar, but some Syrians fear it will work in the new entity to replicate the influence it wields in the narrower Syrian National Council.
The SNC, dominated by the Qatar-backed Brotherhood, agreed under intense U.S. and Qatari pressure on Sunday to become a minority player in a wider body, the Syrian National Coalition.
The new body will try to win international recognition as the sole legitimate representative of the Syrian people and become the main address for political, humanitarian and military support for the revolt against President Bashar al-Assad.
One diplomat on the sidelines of the Doha talks said the Brotherhood, with affiliates in Egypt and Tunisia that have risen to power during the Arab uprisings of the past two years, had been the "swing block" that could make or break the deal.
Sensing the political wind - as an army of U.S and other diplomats deployed in the Qatari hotels where the week of talks took place - the Brotherhood endorsed the new structure.
Opposition to the SNC being subsumed in the new coalition appeared to come largely from secular figures such as its new leader, Christian activist George Sabra.
"The Brotherhood will not monopolise power in the political arena and in managing the coming period," said Farouk Tayfour, a senior Brotherhood figure and deputy SNC leader.
"They will be a part of the overall Syrian framework of rebuilding our country and healing the wounds of Assad family rule."
DOMINATING THE SNC
As in Egypt in the first months after the fall of veteran ruler Hosni Mubarak last year, the Brotherhood tried to play down its influence on the SNC to avoid scaring Western backers.
But accusations emerged that it controlled the body through influence over independent Islamists and was funnelling funds to favoured groups inside Syria to build up its presence further.
With the SNC expected to take around two fifths of the 60 or so seats in the new National Coalition, the Brotherhood's influence is set on paper at least to diminish.
The coalition's first elected head is Mouaz Alkhatib, a popular Islamist preacher from Damascus.
Khatib, 50, has been a regular guest on Qatar's Al Jazeera satellite channel, used by the influential Gulf Arab state to promote Brotherhood-linked Islamists and help facilitate U.S. acceptance of the Islamist network.
Hassan Hassan, a Syrian commentator based in the United Arab Emirates, said he believed Khatib was a true independent, not under Brotherhood sway, but the jury was still out on whether the group would be able to dominate the new National Coalition.
"This is the million dollar question," he said. "When the United States presented this new plan, the Brotherhood knew it could not insist on the survival of the SNC, so they started to build a place for themselves in the coalition - and succeeded."
Many prominent figures resigned from the SNC in recent months complaining that Islamists were sidelining minorities and women. Another three left in Doha, including SNC founder Adib Shishakly, angered over the failure of women to make it onto the SNC's new general secretariat elected last week.
The Brotherhood, whose Syria branch was founded in 1936, says it is simply an effective organiser, and some opposition figures conceded that much of the grumbling reflects personal grudges from individuals lacking popularity.
"They said it was becoming a Brotherhood council. But honestly I think it was because they were not elected (to the secretariat)," one member said of last week's walk-outs.
JURY OUT ON 'COALITION'
Still, respected figures in the new coalition remained mistrustful of the Islamists, whatever their public utterances.
"Right now the Brotherhood is not becoming more open (to other groups). They've said in the past that they would be, but I haven't seen it yet," said leftist dissident Haitham al-Maleh. "They must be pushed to become more open."
Secularists are suspicious of the Islamists' position on women and non-Muslims in an uprising marred by sectarianism.
Assad has drawn support from Christians, Druze, Shi'ites and his own minority Alawites, who fear what the Sunni majority under Islamist influence could have in store for them.
Al Qaeda fighters from Iraq and jihadists from other countries have piled into Syria to join the fight against a ruler they consider infidel because he is an Alawite.
Many Sunni preachers use anti-Alawite rhetoric, spurning the Muslim credentials of a sect distantly linked to Shi'ite Islam.
The Brotherhood clashed with Assad's father Hafez in 1982, when thousands were killed in a failed uprising. It then worked assiduously to build up grassroots influence through mosques and religious schools, despite being a banned organisation.
Syria, which once prided itself as a bastion of secular Arab nationalism, has become religiously conservative.
The Brotherhood has distanced itself from jihadi groups and sectarianism on the ground in Syria, and opposition figures in Doha tried generally to play down Western fears of radicalism.
A rebel military commander dismissed concerns over the Al Nusra Front, a Salafi militia which has carried out suicide attacks, describing them merely as "organised Islamists".
Hassan said opponents remain concerned that, with Qatari support, the Brotherhood could still convince Western powers that it is as influential and powerful on the ground as the Muslim Brotherhood in Egypt, a premise he questioned.
"We all of a sudden have a revolution in Syria, and a lot of groups presented themselves as the one with great influence in society," he said. "But almost 70 percent of the country is outside the reach of the Muslim Brotherhood, if you consider religious minorities, the Kurds and the tribes."