(Reuters) - The Muslim Brotherhood is reaching out to rivals including politicians knocked out of the presidential race in an attempt to rally support around its own candidate who faces a runoff against Hosni Mubarak´s last prime minister, Ahmed Shafiq.

Warning of "determined efforts to recreate the old regime," the Brotherhood said parties that supported the uprising that swept Mubarak from power must unite "so that the revolution is not stolen from us."

The Brotherhood´s presidential candidate, Mohamed Mursi, beat the rest of the field in the first round of the election, with Shafiq a close second, according to an unofficial Brotherhood tally of the vote count. Official results are due out on Tuesday.

The outcome sets up a June 16-17 ballot box struggle between a former air force commander who has described Mubarak as a role model and an Islamist group the deposed leader dealt with mostly as an enemy of the state.

In an apparent overture to the group he is set to face in the runoff, Shafiq told Egyptian television on Friday he saw no problem with the idea of a Muslim Brotherhood-led government if he were elected president.

The runoff will be a historic moment for Egypt and the region, giving voters the choice between a continuation of rule by men from a military background and a government led by a long-oppressed Islamist group with broad regional influence.

It is a choice that many Egyptians are not relishing, either out of fear that a Shafiq victory would mark a blow to hoped-for reform or out of worry a Brotherhood victory would steer the country towards fundamentalist rule.

The army council that has been governing since Mubarak stepped down is due to hand power to the president on July 1 - officially the last stage in a messy and sometimes bloody transition to civilian rule overseen by the generals.

Although the Brotherhood and Shafiq came out on top in the first round, held on Wednesday and Thursday, the unofficial results showed the race to have been very tight, with fewer than 8 percentage points separating the top four candidates.

The 25 percent won by Mursi was a less spectacular outcome for the Brotherhood than the result of the parliamentary elections in which the group won close to half the seats, hinting at a decline in its popularity in the past six months.

The presidential election result also indicated a strong showing by reform-minded independents who between them won more votes than either Shafik or Mursi, underlining the growth of a new centre in Egypt´s fast-evolving political landscape.

"The Brotherhood will have to reach out in a grand and dramatic way to the centre and the other political parties if they have any hope of winning their support and any hope of winning the presidency," said Elijah Zarwan of the European Council on Foreign Relations think tank.

´WE WILL SUCCEED´

The third-and fourth-place contenders - leftist Hamdeen Sabahi and independent Islamist Abdel Moneim Abol Fotouh - were among the politicians the Brotherhood would invite to a preliminary meeting on Saturday, a Brotherhood official said.

The initiative marked a new attempt by the Brotherhood to reach out to other forces that have accused it of seeking to dominate public life since Mubarak was toppled - a charge the group fiercely denies.

There was no immediate word on whether either would attend the meeting at which a Brotherhood party official, Yasser Ali, said the question of the vice presidency and a new coalition government would be discussed.

"We know that we will succeed in uniting behind the initiative to save the nation and to complete the revolution," Essam el-Erian, the deputy leader of the Brotherhood´s Freedom and Justice Party, said during a news conference.

Although a leading voice for years in the Egyptian reform movement, the Brotherhood has appeared increasingly isolated from other parties since the uprising, first facing accusations it was slow to join the revolt and then that it acquiesced in the military rule that followed.

Trust in the Brotherhood was further undermined when the group decided at the 11th hour to join the presidential race, a decision that marked a retreat from its previous pledge not to run. The group, founded in 1928, says it is the target of a vicious smear campaign orchestrated by its opponents.

Losing Islamist candidate Abol Fotouh, who won about 17.6 percent of the vote by the Brotherhood´s count, said in a statement he would now back the Islamist group with which he parted ways last year to pursue his presidential bid.

Abol Fotouh did not name the Brotherhood, but said he and his supporters would "rise above our political and party differences" and would "stand in a united front against the symbols of corruption and oppression," referring to Shafiq.

Shafiq has won support among Egyptians who see him as the kind of strong man the country needs to put an end to 15 months of political instability and other problems including a crime wave.

His constituency also includes Christians, who form about a tenth of Egypt´s 82 million people. They complained of discrimination in Mubarak´s day, but are likely to vote for Shafiq in preference to an Islamist.

Mohamed Habib, a former deputy leader of the Brotherhood who left the group last year in protest at its post-uprising policies, said the group should offer vice presidential positions to at least two people from outside the group.

He suggested one could be a Christian - an idea to which Mursi himself has said he is not opposed.

Habib voted for Abol Fotouh in the first round, but said he would now vote for Mursi. "There is no other option. You are picking between two options. You pick the best of the worst, as they say."

(Additional reporting by Ahmed Tolba; Writing by Tom Perry; Editing by Peter Cooney) (© Thomson Reuters 2012. 05/25/12)