By Paul Taylor

CAIRO/PARIS, July 16 (Reuters) - Mohamed Mursi might still be president of Egypt today if he had grasped a political deal brokered by the European Union with opposition parties in April, Egyptian politicians and Western diplomats say.

Convinced that election victories gave them a sufficient basis to rule, Mursi and his Muslim Brotherhood spurned the offer to bridge the most populous Arab nation's deep political divide. Less than three months later, the army overthrew him after mass anti-government protests.

Under a compromise crafted in months of shuttle diplomacy by EU envoy Bernardino Leon, six secular opposition parties would have recognised Mursi's legitimacy and agreed to participate in parliamentary elections they had threatened to boycott.

In return, Mursi would have agreed to replace Prime Minister Hisham Kandil and five key ministers to form a technocratic national unity cabinet, sack a disputed prosecutor general and amend the election law to satisfy Egypt's constitutional court.

The failure to clinch a deal shows the challenge facing the EU as it seeks to raise its profile in an area where the United States was long the sole power broker. But given deep antipathy to Washington on both sides of Egyptian politics, the EU may be the only "honest broker" and it is not giving up.

Its foreign policy chief, Catherine Ashton, returns to Cairo on Wednesday in a fresh effort to forge consensus - though there was little sign of that on Tuesday when an interim government was sworn in and the Brotherhood denounced it as "illegitimate".

DEAL "CAME CLOSE"

People familiar with the talks said Saad el-Katatni, leader of the Brotherhood's political wing, helped negotiate the deal but could not sell it to Mursi and key Brotherhood leaders.

"We did our best to reach an agreement. We came very close, but in the end Mursi's position didn't change," Hamdeen Sabahi, leader of the left-wing party Popular Current, told Reuters. "He demanded an unconditional dialogue without prerequisites, agenda or objectives.

"If Mursi had accepted these confidence-building steps, the opposition pledged to fully acknowledge his legitimacy and enter parliamentary elections," Sabahi said.

The outline deal, a draft of which was seen by Reuters, would also have endorsed a stalled $4.8 billion International Monetary Fund (IMF) loan. That in turn could have unlocked wider economic aid and investment in the shattered economy.

Mursi, Katatni and senior aides are detained by the army at unknown locations and cannot tell their side of the story.

However, right until the moment the military toppled him on July 3, the president went on proclaiming his electoral legitimacy and showed no signs of willingness to share power.

In his final public appearances, after the head of the armed forces had gone public on June 23 to call for a political truce, Mursi accused his opponents of rejecting various offers he made.

Asked in March about Leon's mediation bid, Mursi's national security adviser, Essam El-Haddad, told Reuters: "We are always open, however the opposition are putting conditions to enter dialogue. Indeed they can't even agree among themselves."

U.S. BACKED INITIATIVE

The United States threw its weight behind the EU initiative rather than trying to forge a deal of its own.

This was partly because the Muslim Brotherhood suspected Washington of plotting with the army against it, while the secular opposition and anti-Islamist Egyptian media accused the Americans of being in cahoots with the Brotherhood.

U.S. Secretary of State John Kerry telephoned Mursi in March and said he supported the European drive, diplomats said. U.S. ambassador Anne Patterson accompanied Leon to a meeting with Mursi a few days later, underlining Washington's endorsement.

Mursi never rejected the EU proposal outright, participants said. But either he was too stubborn or he was unable to reach a consensus in the Muslim Brotherhood leadership in favour of it, and events intervened to blow the initiative off course.

"There was a well described, detailed proposal accepted by all elements of the (opposition) National Salvation Front, which was sent to Mursi," a person involved in the talks said. "We never got an answer."

The proposal was at the heart of a visit to Cairo on April 7 when Ashton had separate meetings with Mursi and the main opposition leaders. Her mission was overshadowed by sectarian violence outside Cairo's Coptic cathedral, which further undermined opposition trust in Mursi and the Brotherhood.

On that trip, Ashton also met armed forces commander General Abdel Fattah al-Sisi, the man who led the military intervention to oust Mursi. Participants said Sisi had also supported the EU initiative, saying the army did not want to intervene in politics and would welcome a broader national consensus.

"Contrary to what the Brotherhood is saying now, the army did its best to keep Mursi in office," one participant said.

GOODWILL

Mursi did make some goodwill gestures to the opposition but he did not go far enough to break the deadlock. When the constitutional court rejected the election law passed by the Islamist-dominated upper house of parliament, he agreed to put back parliamentary elections from April until late in the year.

He also hinted he was willing to change the reviled prosecutor, accused of Islamist bias, but never actually did so.

Other incidents combined to deepen mistrust between Mursi and the opposition, and put a deal out of reach.

"The main problem was that there was a complete lack of trust among all of them," a European diplomat said.

The Brotherhood's Freedom and Justice newspaper splashed an article accusing senior liberal politician Mohamed ElBaradei of receiving massive funds from the United Arab Emirates. A National Salvation Front statement branded Mursi a "fascist".

Mursi's party, which saw the judiciary as packed with supporters of ousted dictator Hosni Mubarak bent on obstructing its policies, backed another Islamist party's bill to remove 3,000 judges by lowering their retirement age to 60 from 70.

The opposition denounced a Brotherhood power grab. When Mursi eventually reshuffled the cabinet, he kept the widely criticised Kandil and made no opening to the opposition.

Leon, a former Spanish and EU diplomat steeped in the Arab-Israeli peace process, was appointed EU special representative for the Southern Mediterranean in 2011 after the Arab Spring uprisings in Tunisia, Egypt, Libya, Yemen and Syria.

He wielded neither the big chequebook nor the military firepower and military-to-military relations that underpin U.S. diplomacy. Leon's advantage, acknowledged by Muslim Brotherhood officials now ejected from office, was that he was seen by all sides as an honest broker. But he never managed to "deliver" the Brotherhood to a deal its leaders were not sure they wanted. (Additional reporting by Tom Perry, Edmund Blair and Yasmine Saleh; Writing by Paul Taylor; Editing by Alastair Macdonald)