(Reuters) - Demonstrators furious that Hosni Mubarak´s last prime minister made it into the run-off for Egypt´s presidential election set ablaze his campaign headquarters on Monday, witnesses said, underscoring the divisive outcome of the country´s historic vote.

Former air force commander Ahmed Shafiq, who has described Mubarak as a role model, will face the Muslim Brotherhood´s Mohamed Mursi in the run-off. It is a contest between the two most polarizing and controversial figures in the race.

A group of protesters broke into and vandalized Shafiq´s office in the residential district of Dokki before setting it ablaze, the state news agency reported. An official in the fire service confirmed the blaze had been extinguished without causing any casualties.

Several thousand protesters took to the streets across Egypt to demonstrate against the result of the election´s first round, which was officially announced on Monday.

Trouble flared in Cairo´s Tahrir Square when activists said unknown assailants attacked one such protest. Rocks flew in scenes reminiscent of other spasms of violence during a messy transition from military rule that is due to end when the military hands power to the new president on July 1.

Local media reported the protest had been attacked by unknown "thugs", though the account could not be independently confirmed.

Many analysts had predicted that a Shafiq-Mursi run-off could trigger trouble. The vote marks a ballot box struggle between a symbol of the military-based autocracy of the last six decades and one of the Islamist movements it had oppressed.

The result is deeply disappointing to the activist movement that took to the streets on January 25, 2011, triggering the mass uprising that toppled Mubarak. They had seen other candidates as more representative of their hopes for change.

One of those candidates, Khaled Ali, joined the protest in Tahrir, "(The elections) were neither free or fair," Ali told news channel Al Jazeera Mubasher Misr, adding that Tahrir was the place that had "toppled Mubarak, and would topple Shafiq".

Shafiq has built a sizeable constituency with a law-and-order platform, convincing some he is the man to end 15 months of turbulence. Mursi´s supporters believe Mursi and the Brotherhood are the best hope for reforming a corrupt state.

But many Egyptians picked neither and are now left with a wrenching choice between a symbol of the past and an Islamist group that arouses deep suspicions for some.

Mursi topped the poll with 24.3 percent of the vote, followed by Shafiq with 23.3 percent. Turnout was 46 percent, according to the official results.

About half of the first-round votes went to candidates somewhere in the middle ground - from leftist Hamdeen Sabahy, third-placed with 20.4 percent, to moderate Islamist Abdel Moneim Abol Fotouh, with 17.2 percent, and former Arab League Secretary-General Amr Moussa, with 10.9 percent.

´QUESTION MARKS´

Mahmoud Momen, a 19-year-old student, held aloft a picture of Shafiq with a black X daubed over his face as he took part in a Cairo march against the result.

"Neither Brotherhood or feloul," he said, invoking the word used in Egyptian political slang to refer to politicians who served in the Mubarak administration. "We want someone who represents the square."

Another protester, a 19-year-old student who identified himself as Omar, said the vote had been rigged, triggering an argument with a bystander who disputed the claim.

Similar protests erupted in Alexandria on Egypt´s northern Mediterranean coast, and in Port Said, Ismailia and Suez, cities along the Suez Canal east of Cairo.

In Alexandria, some 2,000 protesters marched through the city, tearing up Shafiq and Mursi election posters they encountered along their way.

The protests were fuelled by accusations - denied by the committee overseeing the vote - that there had been serious violations. Abol Fotouh, Sabahy and Moussa filed complaints about the voting, all of which were rejected by the committee.

Earlier, Abol Fotouh alleged the vote had been marred by vote buying and other irregularities. "I reject these results and do not recognize them," said Abol Fotouh, a former Brotherhood member. In a statement, Sabahy also alleged irregularities.

Moussa said earlier that "question marks" hung over the vote. "There were violations, but this should not change our minds on democracy and the necessity of choosing our president."

The Muslim Brotherhood sought to muster a coalition to help Mursi against Shafiq.

The close contest has set both contenders scrambling for support, particularly the Muslim Brotherhood, which is trying to draw losing candidates and other political forces into a broad front to prevent a "counter-revolutionary" Shafiq victory.

The ultra-orthodox Salafi Islamist party Al-Nour has said it will now back Mursi, after siding with Abol Fotouh in the first round. The party has the second biggest bloc in parliament after the Brotherhood´s Freedom and Justice Party.

Beyond the Islamist movement, it might prove harder for the group to find allies. Secular-minded parties have grown suspicious of the Brotherhood, accusing it of being power hungry and putting a quest for power over principle - charges it denies.

A Brotherhood source, who asked not to be named, said the Islamist group had prepared a menu of options to tempt rival groups and politicians to its side.

These include creating a five-member advisory council to advise the president; assigning the posts of prime minister or vice-president to Abol Fotouh and Sabahy; distributing cabinet posts to other parties; and offering compromises on planned laws and on an assembly tasked with drafting a new constitution.

(Additional reporting by Marwa Awad, Tamim Elyan, Shaimaa Fayed, Dina Zayed, Edmund Blair, Patrick Werr in Cairo and Abdel Rahman Youssef in Alexandria; Writing by Alistair Lyon and Tom Perry; Editing by Mark Heinrich and Eric Beech) (© Thomson Reuters 2012. 05/28/12)