By Yasmine Saleh and Shaimaa Fayed
CAIRO (Reuters) - Supporters of Egypt's deposed Islamist president rallied in the thousands in Cairo on Thursday to celebrate the Eid al-Fitr holiday and demand his restoration as the military held back from breaking up their protests.
The rarely-seen wife of the ousted Mohamed Mursi, Naglaa Mahmoud, made a surprise appearance on stage at the main demonstration in Cairo to appeal for her husband to be allowed back into power as crowds roared "Return! Return!"
But crowds also filled Tahrir Square in a show of support for the military and the interim government it installed after overthrowing Mursi five weeks ago.
The political crisis has reached a dangerous new phase following the collapse this week of an international effort to bridge the gap between the two sides and avert bloodshed.
But the four-day Eid holiday at the end of the Muslim fasting month of Ramadan started in a festive and largely peaceful atmosphere. By late afternoon, no violence had been reported.
Sheikh Gomaa Mohamed Ali led prayers at Tahrir Square and spoke out against further bloodshed. He called on Mursi supporters to abandon their protest camps at the Rabaa Al-Adawiya Mosque and Cairo's Nasr City.
Interim President Adly Mansour had on Wednesday warned the protesters to leave the camps or face action, saying government patience was running out. He also declared that the mediation effort by U.S.. European and Arab envoys had failed.
However, a person involved in the diplomatic push said the authorities and Mursi's Muslim Brotherhood might yet step back from confrontation and implement mutual confidence-building steps that could lead to a negotiated settlement.
"It's not over yet," the diplomat said. "It could work but we don't have any guarantees. Everything is very fragile."
Government and military sources said the talks had not terminated but had been frozen, to assuage public anger over perceived foreign interference in Egypt's affairs and the authorities' willingness to negotiate with the Brotherhood.
A military source said the authorities were holding back from using force to clear the protest camps partly due to fear that liberal Vice President Mohamed ElBaradei would resign, removing a source of political legitimacy for army rule.
Interim Prime Minister Hazem el-Beblawi visited the Central Security Forces on Thursday in an apparent effort to calm hardliners impatient for tougher action.
"He assured them that the government places security at the top of its priorities," a statement from Beblawi's office said.
Mursi has been detained at a secret location since the military removed him from power on July 3. Other senior Brotherhood figures have also been rounded up.
Thousands of men, women and children converged on the Brotherhood protest camp at Rabaa in a festive atmosphere to attend prayers and a rally on the first day of Eid.
The public appearance of Mursi's wife after five weeks out of the limelight caused wild excitement outside the Rabaa al-Adawiya mosque. With her was senior Brotherhood leader Mohamed El-Beltagi.
"God willing he is returning, God willing, God willing," she said. "Praise God, the Egyptian people proved that they are Islamist."
An undercurrent of fear still ran through the camp.
"Military coups are always carried out through the use of force. So there's always a danger they could use violence." said Abdelatif Mohamed, 32.
Mohamed Nabil, 60, said the authorities could use violence to break up the protest, but not on the first day of Eid.
Supporters of the new government rallied in Tahrir Square, the focal point of the uprising that brought down strongman Hosni Mubarak in February 2011, to celebrate what they consider a second revolution.
Awad Abdel Gawad, a 60-year-old woodworker, said: "I am here to say happy Eid to the people of the revolution, of Tahrir Square. Every revolution has troubles at the start but God will help us."
Mursi supporters should give up, he said.
"The Rabaa people think Mursi's coming back but he isn't. He is gone," Abdel Gawad said.
Mursi took power as Egypt's first democratically-elected president in June 2012. But fears he was trying to set up an Islamist autocracy and his failure to ease economic hardships led to mass street demonstrations which triggered the army move.
Almost 300 people have been killed in political violence since the overthrow, including dozens of Mursi supporters shot dead by security forces in two incidents.
In one apparent conciliatory gesture, prosecutors dropped the main charge against the head of the Brotherhood's political wing, Saad El-Katatni, in a possible prelude to releasing him.
So far, the Brotherhood has refused to accept what it calls the illegal coup and has publicly demanded Mursi's return.
The new authorities have accused Islamist leaders of inciting violence, frozen the Brotherhood's assets and said they will put them on trial.
"The train of the future has departed, and everyone must realise the moment and catch up with it, and whoever fails to realise this moment must take responsibility for their decision," interim president Mansour said in an Eid broadcast.
Diplomats have said any settlement would have to involve a dignified exit for Mursi, Brotherhood acceptance of the new situation, the release of political prisoners arrested since the takeover, and a future political role for the Brotherhood.
The United States and the EU expressed concern on Wednesday that the Egyptian parties had not found a way to break what they called a dangerous stalemate.
"This remains a very fragile situation," U.S. Secretary of State John Kerry and EU foreign policy chief Catherine Ashton said in a statement.
(Additional reporting by Maggie Fick, Omar Fahmy and Alex Dziadosz in Cairo and Paul Taylor in Paris; Editing by Angus MacSwan and Andrew Roche)