ISTANBUL - At a meeting of Syria's opposition, Muslim Brotherhood officials gather round Marxists colleagues, nudging them to produce policy statements for the Syrian National Council, the main political group challenging President Bashar al-Assad. With many living in the West, and some ditching their trademark beards, it is hard to differentiate Brotherhood from leftists. But there is little dispute about who calls the shots. From annihilation at home 30 years ago when they challenged the iron-fisted rule of Hafez al-Assad, the Brotherhood has recovered to become the dominant force of the exile opposition in the 14-month-old revolt against his son Bashar. Careful not to undermine the council's disparate supporters, the Brotherhood has played down its growing influence within the Syrian National Council (SNC), whose public face is the secular Paris-based professor Bourhan Ghalioun. "We chose this face, accepted by the West and by the inside. We don't want the regime to take advantage if an Islamist becomes the Syrian National Council's head," former Brotherhood leader Ali Sadreddine al-Bayanouni told supporters in a video. The footage is now being circulated by Brotherhood opponents, seeking to highlight its undeclared power. "We nominated Ghalioun as a front for national action. We are not moving now as Muslim Brotherhood but as part of a front that includes all currents," said Bayanouni. The Syrian Brotherhood is a branch of the Sunni Muslim movement founded in Egypt in the 1920s. It was a minor political player before a 1963 Baath Party coup but its support grew under the authoritarian 30-year rule of Hafez al-Assad, as his minority Alawite community dominated the majority Sunni country. Mindful of international fears of Islamists taking power, and of the worries of Syria's ethnic and religious minorities, the Syrian Brotherhood portrays itself as espousing a moderate, Turkish-style Islamist agenda. It unveiled a manifesto last month that did not mention the word Islam and contained pledges to respect individual rights. With backing from Ankara, and following the political ascendancy of the Brotherhood in Egypt, Tunisia and Libya since Arab Spring revolts broke out two years ago, the group is poised to be at the top of any new governing system in Syria. Extending the loose Brotherhood umbrella to Syria will raise pressure on the U.S.-backed Hashemite monarchy in Jordan, where the local Brotherhood has been sidelined by laws that favor tribal politicians allied with the security apparatus. Iraq's Shi'ite rulers could also find they have a hardline Sunni government as their neighbor, and Lebanon's Shi'ite guerrilla group Hezbollah would lose its main Arab backer. Working quietly, the Brotherhood has been financing Free Syrian Army defectors based in Turkey and channeling money and supplies to Syria, reviving their base among small Sunni farmers and middle class Syrians, opposition sources say. "We bicker while the Brotherhood works," said Fawaz al-Tello, a veteran opposition figure who is a pious Muslim while being on the liberal end of the Syrian political spectrum. "They have gained control of the SNC's aid division and the military bureau, its only important components," said Tello, a former political prisoner who fled Syria four months ago. "But they still have to work more do to get support on the inside. Lots of clerics, activists and rebels do not want to be linked to them." Tello, however, acknowledged that the Brotherhood has clawed back influence inside Syria, especially in the cities of Homs and Hama and the rural province of Idlib on the border with Turkey, hotbeds of the revolt against Assad. This is no small feat after three decades in the political wilderness. Unlike Arab rulers who tried to co-opt the movement by granting it limited operation, the Assads excluded it and all other opposition from the political system. Bashar's father Hafez al-Assad's forces killed, tortured and imprisoned tens of thousands of people after leftists and Islamists began challenging his rule in the 1970s. The Brotherhood took the brunt of the repression, and a 1980 decree singled out membership as punishable by death. Mulhem Droubi, educated in Canada and one of a younger generation of Brotherhood leaders, said the group is not primarily concerned with political prominence. "We are a party that presents moderate solutions. We are not extremists, neither to the left nor to the right and our program is the most accepted by the Syrian street," he said. "We are working for the downfall of Bashar al-Assad and not to find a popular base. We leave competition for the future in a free Syria," the softly spoken Droubi told Reuters.