(Reuters) - Egyptian presidential hopefuls Amr Moussa and Abdel Moneim Abol Fotouh traded barbs about their past in a debate that captured the historic moment facing a nation preparing for its first real election for head of state.

Viewers tuned in across the Arab world for a spectacle unthinkable before Hosni Mubarak was swept from power by a mass uprising 15 months ago. The election gets under way in two weeks, the climax of an army-led transition to civilian rule.

One a veteran diplomat who once served as Mubarak´s foreign minister and the other an Islamist who was jailed by his administration, Abol Fotouh and Moussa have emerged as two of the leading contenders to replace the deposed president.

Facing off for more than four hours in a show broadcast on two privately owned television networks, Moussa and Abol Fotouh sought to trip each other up on questions ranging from their perspective on Islamic sharia law to their views on Israel. They repeatedly accused each other of distorting the facts.

A former member of the Muslim Brotherhood, Abol Fotouh portrayed Moussa as a member of the Mubarak government that had corrupted Egypt. "There is a rule that says the that one who created the problem cannot solve it," said the 60-year old.

Moussa, who was head of the Arab League at the time of the uprising, defended his record as Egypt´s foreign minister but added that he had left the post in 2001. "The regime that fell, fell with Moussa outside of it," said the 75-year old. "I say, you too were silent. You used to defend the positions of the Muslim Brotherhood and not Egyptian interests."

Egyptians are due to vote on May 23 and 24 in the first round of the election that is expected to go to a June run-off between the top two candidates from the field of 13.

The first real presidential election in this country of more than 80 million people is being watched across the region as a measure of change brought by last year´s historic uprisings across the Middle East.

Other contenders include Mohamed Mursi, the Muslim Brotherhood´s candidate, Ahmed Shafiq, Mubarak´s last prime minister, and Hamdeen Sabahy, a leftist. The organizers of Thursday´s debate said Moussa and Abol Fotouh had been invited because they were ahead in the polls.

ISLAMIC LAW, ISRAEL

Abol Fotouh has sought to build a broad constituency encompassing moderate and hardline Islamists, the centre ground and some reform- minded liberals. Moussa appeals to voters who believe Egypt needs someone of experience at the helm and who worry about the consolidation of Islamist influence.

Both are competing for the many undecided voters whose choices will prove decisive.

During a 90-minute build-up to the show, the broadcasters set the historical scene by screening archive footage of the 1960 U.S. presidential debate between John F. Kennedy and Richard Nixon - the first ever televised presidential debate.

In a cafe in a working class district of Cairo, supporters of the rivals broke into arguments during the breaks. While they disagreed on politics, they saw the debate as a good thing.

"The debates decide winners in the United States. We want that in Egypt," said Ahmed Hussein, a student who will vote for Abol Fotouh. "It is a good thing for people to see and form an opinion," added Hassan Abdel Aal, a contractor voting Moussa.

Both bespectacled and dressed in suits and ties, Abol Fotouh and Moussa touched on taxation, police reform, education, the health care system and the role of the powerful military - which they both said should stay out of politics.

Moussa said he was the statesman Egypt needed to lead it through "a crisis of existence". Abol Fotouh said he was the man to unite the country and end "a state of polarization" between liberals, leftists and Islamist.

Each pushed the other to clarify their views on Islamic law. Abol Fotouh asked questions of Moussa that suggested he was soft on sharia. Moussa in turn intimated that Abol Fotouh was saying different things to different people on the subject and suggested he was more radical than he was letting on.

Both pledged to review Egypt´s 1979 peace treaty with Israel, a country Abol Fotouh described as an enemy and Moussa called an adversary. As the debate moved to foreign policy in the early hours of the morning, the veteran diplomat Moussa made a gaffe when he called Iran an Arab state.

A TENSE FINALE

The debate repeatedly swiveled back to their past lives.

Moussa asked Abol Fotouh about an oath he had pledged to the religious guide of the Brotherhood. "What does this oath mean? Does it mean that if you are elected you will have (another) president?" he said.

Abol Fotouh replied: "It seems Amr Moussa doesn´t follow the news carefully and doesn´t know that I resigned from the Muslim Brotherhood after I decided to run for the presidency in April, 2011. This resignation was because I wanted to be free to serve the nation - to be a president for all Egyptians."

Moussa accused him of double-speak, asking how he had managed to win endorsement from both liberals and hardline Salafi Islamists. "With Salafis, he is a Salafi. With liberals, he is a liberal. With centrists, he is a centrist," he said.

The tension which appeared to build through the debate manifested itself in scathing closing remarks.

Moussa urged Egyptians not to vote for a man he said was unclear in his policies and was not qualified to lead a state, accusing him of "forging history".

"I am sorry to say that we must warn the Egyptian people," Moussa said. "The next president must have certain qualifications that can lead the country."

Abol Fotouh shot back by saying that a vote for Moussa would be a step backwards. "We are for the first time choosing the president of Egypt," he said. "I hope that we don´t allow ourselves to be taken back, once again, to the fallen regime, with its ideas, its substance and figures," he said.

(Additional reporting by Tamim Elyan and Edmund Blair; Writing by Tom Perry. Editing by Christopher Wilson) (© Thomson Reuters 2012. 05/10/12)