* Islamic scholar convenes Muslim Brotherhood, opponents
* Talks follow week of violence with nearly 60 dead
* Political leaders sign document renouncing violence (Adds quotes from politicians, call for more protests)
By Tom Perry and Peter Graff
CAIRO, Jan 31 (Reuters) - Egypt's feuding politicians renounced violence on Thursday after being summoned by the country's most influential Muslim scholar to talks to end the deadliest unrest since President Mohamed Mursi took power.
It remains to be seen whether the pledge to end confrontation will halt a week of bloodshed on the streets that killed nearly 60 people. Opposition groups did not cancel new demonstrations scheduled for Friday.
But participants at the meeting, including leaders of Mursi's Muslim Brotherhood and its secular rivals, described their joint statement as a major step towards ending a conflict that has made the most populous Arab state seem all but ungovernable two years after an uprising toppled autocrat Hosni Mubarak.
The meeting was convened by Sheikh Ahmed al-Tayyeb, head of the thousand-year-old al-Azhar university and mosque, one of the few institutions still seen as neutral in a society that has become increasingly polarised.
He told politicians that a national dialogue, "in which all elements of Egyptian society participate, without any exclusion, is the only tool to resolve any problems or differences.
"Political work has nothing to do with violence or sabotage and the welfare of everyone and the fate of our nation depends on respect for the rule of law," the sheikh said.
Participants signed a document pledging to renounce violence and agreed to set up a committee of politicians from rival groups to work out a programme for further talks.
"We come out of the meeting with a type of optimism," liberal politician Mohamed ElBaradei said. "Each of us will do what we can, with goodwill, to build trust once again among the factions of the Egyptian nation."
Saad el-Katatni, head of the Brotherhood's Freedom and Justice Party, called it "an historic day".
"Everyone in the meeting expressed readiness to make concessions to make this experiment succeed," he said.
Al-Azhar, one of the main seats of learning in Sunni Islam worldwide, has tended to keep itself above Egypt's political fray. Its extraordinary intervention follows a warning by the army chief on Tuesday that street battles - which erupted last week to mark the second anniversary of the uprising that toppled Mubarak - could bring about the collapse of the state.
SPIRIT OF THE REVOLUTION
The opposition accuses Mursi of betraying the spirit of the revolution by concentrating too much power in his own hands and those of the Brotherhood, a decades-old underground Islamist movement banned under Mubarak. The Brotherhood accuses its foes of trying to topple Egypt's first elected leader.
Participants at Thursday's meeting included Katatni and the Brotherhood's deputy leader Mahmoud Ezzat. Television footage showed them sitting opposite liberals ElBaradei and Amr Moussa, respectively former heads of the U.N. nuclear watchdog and the Arab League, and leftist Hamdeen Sabahi.
The streets have grown quieter in the past few days, and on Wednesday authorities scaled back a curfew imposed on three Suez Canal cities where most of the week's blood was spilt.
Nevertheless, even as Thursday's meeting was under way, a statement issued by opposition parties including Sabahi's Popular Current reiterated a call for demonstrations at the presidential palace in Cairo on Friday.
"The wave of revolutionary anger that erupted in the Egyptian provinces to express the Egyptian people's rejection of the continuation of the same policies - even if the faces have changed - will continue and go on to stress its legitimate demands in achieving the goals of the revolution," it said.
Attending the meeting was a partial reversal for the opposition alliance, which had previously spurned Mursi's call for talks, demanding that the president first agree to include opponents in a national unity government.
"Discussions concluded that there is no solution to the problems of the nation's democratic transition other than through dialogue, and dialogue must have foundations and guarantees, and not preconditions," the Brotherhood's Katatni said.
The secularists are nonetheless likely to continue to press for inclusion in a national unity government, a call also backed by the hardline Islamist Nour party in an unlikely alliance of Mursi's critics from opposite ends of the political spectrum.
The Brotherhood rejects a unity government as an attempt by Mursi's foes to take power they could not win at the ballot box.
The crisis forced Mursi to cut short a visit to Europe on Wednesday that had been intended to lure investment to Egypt. While in Berlin, the president sidestepped calls for a unity government, saying the next cabinet would be formed after parliamentary elections due in April.
UNREST TARNISHES MURSI'S RISE
The rise of an elected Islamist president in the Arab world's most populous state after generations of secularist military rule is probably the most important outcome of the wave of Arab revolts over the past two years.
But Mursi's seven-month rule has been tarnished by the civil unrest, worsening an economic crisis that forced Cairo to sell off most of its reserves to keep its currency from crashing.
The past week's violence followed weeks of demonstrations last year against a new constitution, as Mursi failed to unite Egyptians despite the Brotherhood winning repeated elections.
Ejijah Zarwan, who analyses Egyptian politics for the European Council on Foreign Relations, said Thursday's intervention by al-Azhar was important, but it was far from clear whether it would be enough to calm the streets.
"It's a good first step. Certainly it will help the formal opposition to be very clearly on record as opposing violence," he said. But he added: "The people fighting the police and burning buildings are not partisans of any political party. They might not even vote."
"There's a political crisis and there's a social and economic crisis. A negotiated solution to the political crisis will certainly help but it's just a necessary first step towards resolving the social and economic crisis." (Reporting by Tom Perry; Additional reporting by Omar Fahmy and Yasmine Saleh; Writing by Peter Graff; Editing by Paul Taylor)