(Reuters) - The Muslim Brotherhood has deployed a formidable campaign machine in its quest for the Egyptian presidency but faces an uphill struggle winning over voters, hampered by its own image problems and the limited appeal of its candidate, Mohamed Mursi.

A 60-year-old engineer, Mursi has at times appeared ill at ease in the public eye since he was thrust into the race by the disqualification of the Brotherhood´s primary candidate, Khairat al- Shater. Mursi´s critics say he lacks charisma.

The movement to which he belongs is meanwhile trying to fix a broader image problem. It is facing tough criticism from other Egyptians over its handling of the 14 months of military rule that followed Hosni Mubarak´s downfall.

After prayers on Friday, Brotherhood activists deployed outside one Cairo mosque to hand out Mursi campaign pamphlets, accompanied by a leaflet trying to debunk accusations leveled against the group, including the idea it has broken its promises to Egyptians by seeking to monopolize public life.

"We see that our popularity has fallen a bit," said Essam Khalil, a Brotherhood organizer at one campaign event. "But we are on our way to recovering it," he said.

"We have a group of activities going into the street: meeting the people; holding meetings and marches and showing videos in the squares," he added. "Daily, things are improving."

The available opinion polls show Mursi way behind others including ex- Arab League chief Amr Moussa and Abdel Moneim Abol Fotouh, an independent Islamist who parted ways with the Brotherhood last year to pursue his own presidential bid.

The polls reflect the challenge facing the Brotherhood as it seeks to turn its success in legislative elections earlier this year - it won nearly half the seats in parliament - into executive power in the May 23-24 nationwide presidential vote.

Some commentators believe the group has little chance, having fielded a candidate many say has limited appeal outside the Brotherhood faithful at a time when the movement is battling negative perceptions in the broader electorate.

Criticized for stiff and sometimes meandering public addresses, Mursi has been described as a Brotherhood functionary rather than a visionary. His speeches are heavy on religious references that reflect his conservative credentials. But he failed to win the support of the Nour Party, the hardline Islamist party which has endorsed Abol Fotouh.

Yet the Brotherhood says it is still in the race. The Mursi campaign has become very much a team effort that is sending a message this is a presidential bid by a movement, not a man. Its slogan is an "Egyptian renaissance with an Islamic foundation".

Brotherhood leaders say polls in this nascent democracy cannot be trusted. They also point out that their 84-year-old movement has broader and deeper political reach than any of its rivals and that many voters have yet to make up their mind.

"Opinions are changing from one day to the next," said Essam el- Erian, a Brotherhood leader, speaking on the sidelines of a Brotherhood rally in Cairo, organized in the shadow of the oldest mosque in the country. "Dr. Mursi´s strength is in the fact that behind him is a strong party," he added.

"I HEAR AND OBEY"

The Brotherhood´s decision to run came very late. It had been the focus of protracted debate in the group´s advisory council and passed by only a slim majority. Once the decision was made, a large majority picked Shater as the man to run.

But he was disqualified on the grounds of a criminal conviction handed to him in Mubarak´s days.

The strengths and weaknesses of the Mursi campaign were on show this week when the Brotherhood launched his final push for the vote with a mass rally in the industrial city of al-Mahalla al-Kubra in the Nile Delta north of Cairo.

Thousands of supporters, many in Mursi T-shirts, filled the stadium, where hundreds of activists formed lines to control the crowd. It was a show of the organizational strength that helps explain why the group did so well in the parliamentary polls.

Brotherhood supporters waved the movement´s green flag and Egypt´s national colors as deafening chants of "God is Greatest" rose to a climax as Mursi took to the stage, accompanied by Mohamed Badie, the group´s leader.

Badie extolled Mursi´s virtues in his speech, describing him as "a graduate of the Brotherhood nursery".

Mursi, in turn, presented himself as a reluctant latecomer to the race. "I say to you: I hear and obey, even if it is against my desire," he said. "I am walking this path to satisfy God and out of concern for our nation and our people," he added.

Yet by that point, hundreds of the attendees were streaming out of the gate, preferring to beat the rush than hear a man who would be Egypt´s next president.

Outside the ground, meanwhile, an anti-Brotherhood protest illustrated the wider PR problem the group faces.

On the road into Mahalla, there were signs that there is still work to do. A convoy of Mursi activists, their cars plastered with his campaign posters, were welcomed by supporters who had deployed for miles along the road.

But there was also opposition. "The Brotherhood are liars," read one sign strung between two lampposts.

(Additional reporting by Tamim Elyan; Writing by Tom Perry, editing by Diana Abdallah) (© Thomson Reuters 2012. 05/04/12)