ISTANBUL, May 6 (Reuters) - Hundreds of members of the Syrian Muslim Brotherhood have returned from exile, hoping to rebuild a movement which was crushed decades ago at home and is deemed a terrorist organization by leading Arab states.Membership of the Brotherhood remains punishable by death in Syria more than 30 years after President Bashar al-Assad's father outlawed the group, but the exiles are filtering back mainly into opposition-held areas.There they are trying to re-establish the influence and credibility of the movement which has no official military wing and plays down suggestions that it is covertly supporting armed groups fighting in the Syrian civil war."We are encouraging people to go back to Syria... I would say hundreds," Mohammed Walid, who heads the Syrian Brotherhood, told Reuters.Walid said in an interview that these "nuclei" members had to explain the aims of his group, which is an offshoot of the Egyptian Muslim Brotherhood. "We've been absent from the scene for so long now - many people in Syria don't know us much," he said in Istanbul, where he lives.Egypt, Saudi Arabia and the United Arab Emirates classify the wider Brotherhood as a terrorist organization, and it has been excluded from the latest round of UN-led peace talks.However, the Syrian arm says it practices "moderate Islam", distancing itself from radical Islamic State militants who have carved out a self-declared caliphate in Syria and Iraq. Walid, a 70-year-old eye specialist from the port city of Latakia who left Syria in the 1970s, said the returnees had mostly settled in Aleppo, Idlib and Hama.In 1982 security forces under then-president Hafez al-Assad demolished neighborhoods of these northwestern cities and killed thousands of people to put down a Brotherhood uprising.Apart from inactive older members who could not leave, no representation remained in Syria after that, said Omar Mushaweh, a member of the Syrian Brotherhood's leadership.What was once Syria's dominant Islamist movement may one day have to compete with the likes of Ahrar al-Sham and Jaysh al-Islam. These are armed Islamist brigades but they already have political offices and sophisticated media strategies, suggesting they may eventually establish formal political wings.Having seized Idlib city in March, led by Islamist forces, Syrian rebels have made major gains in Idlib province in recent weeks. Government forces, Islamic State and other opposition fighters hold various parts of Aleppo, while Hama city is mostly government-controlled.Some Syrians say the Brotherhood is backing rebel brigades such as Jaysh al Mujahideen."I'm sure they supported Jaysh al Mujahideen and other groups, but since then there has been a negative campaign against the Brotherhood inside Syria," said Yaser Al-Haji, a political activist in Aleppo. "They are not out in the open."One former Brotherhood employee said he believed the Idlib-based Faylaq Sham group was founded and backed by the Brotherhood. "There is Brotherhood everywhere," he said. The Brotherhood is a large body, many of whose members work independently. However, Walid suggested the organization could not afford to provide supplies or money to any fighting groups."We are having a lot of problems with funding our activities ourselves, so I don't think we have enough money to support others," he said, adding that most of its funds came from individuals, with occasional contributions from Brotherhood groups abroad.ESTABLISHED ROOTSIn Egypt, the Brotherhood was once the country's best organized and most successful opposition movement. However, hundreds of its members have been killed and thousands detained since Islamist President Mohammed Mursi was overthrown in 2013.It was a minor political player in Syria before a 1963 coup by the secular nationalist Baath Party. Its popularity grew under the 30-year Baathist rule of Hafez al-Assad, whose minority Alawite community dominated the Sunni Muslim majority."In Syria we only had the Baath Party and the Muslim Brotherhood, so they are more organized and institutionalized than anyone else because they have such a long history," said Adib Shishakly, the Gulf envoy of the Western-backed opposition Syrian National Coalition.But he questioned its ability to capitalize on that. "They don't have a young generation and although there's some recruitment, they're not popular," said Shishakly, whose grandfather persecuted the Brotherhood as Syria's president in the 1950s. "People supported them because they were the only religious option, now there will be lots."Al-Haji said anger over how the Brotherhood's leadership escaped after 1982, leaving hundreds of its members to face execution, was still hurting the movement's popularity.REGIONAL PRESSUREWalid said he hoped Saudi Arabia's mistrust of the Muslim Brotherhood would ease under its new monarch, King Salman, who has pushed for Sunni Muslim nations to set aside differences over political Islam."Maybe some personalities which were hostile to the Islamic trend have been removed from office," Walid said, declining to give details because of diplomatic sensitivities.The Brotherhood is represented by five members of the 110-strong Syrian National Coalition. Walid said they were too few to wield control, despite past complaints from other members that the Brotherhood was too powerful.The United Nations launched on Tuesday a new push to find common ground between the warring parties and for the first time said it hoped armed opposition groups might come to Geneva.Walid said his group had not been invited but that it was not clear whether the aim was more UN-led negotiations or "a report to be put on the shelf".