The military insists it is neutral in the race.
Thousands of Egyptians marched on Monday night in protest after the results of the first round were confirmed by the election committee. "No to Shafiq and to the Brotherhood. The revolution is still in the square," they chanted.
In his bid to broaden the group's appeal beyond its disciplined network of supporters who propelled him to the run-off, Mursi indicated he was offering vice-president posts and even the prime minister's position to people outside his group.
"I am committed to the presidency being an institution. It will never be an individual," Mursi told a news conference.
Mursi, who said in his campaign he would implement Islamic law without spelling out what that meant in practice, sought to assuage some liberal fears by saying no one would force women to wear the hijab, the Islamic veil that many already wear.
Mursi also said he wanted to work with Christians, who make up a 10th of Egypt's 82 million people and fear Islamist rule.
In Cairo, some protesters held posters of Mursi with a cross over his face. But most chanted against Shafiq, who has support from many ordinary Egyptians who want a strongman to restore stability and revive the economy after 15 months of turmoil.
Dozens marched from protests around Tahrir Square, where hundreds of thousands had gathered when toppling Mubarak, to Shafiq's headquarters in the upscale Cairo district of Dokki.
"They seemed to know what they were after and they went directly to the storage rooms and set them on fire using petrol bombs," said Ahmed Abdel Ghani, 30, a member of Shafiq's campaign, surveying a scene of unusable, charred campaign flyers and leaflets scattered on the ground.
The main villa escaped the flames but protesters smashed laptops and computers inside, he said. Daubed on the wall outside the villa were the words: "No to Shafiq, no to feloul," an Arabic word referring to "remnants" of Mubarak's era.
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