By Yasmine Saleh and Angus MacSwan
CAIRO (Reuters) - The Muslim Brotherhood has rejected pleas from international envoys to "swallow the reality" that Mohamed Morsi will not return as Egypt's president, the Brotherhood spokesman said on Monday.
The envoys, trying to resolve a political crisis brought on by the army's overthrow of the Islamist Morsi a month ago, had visited jailed Brotherhood deputy leader Khairat El-Shater in the early hours of Monday.
But he cut the meeting short, saying they should be talking to Morsi, spokesman Gehad El-Haddad said.
From the other side, a senior military source said the army and interim government would offer to free some Muslim Brotherhood members from jail, unfreeze its assets and give it three ministerial posts in a move to end the crisis.
Meanwhile several thousand Islamist supporters marched through downtown Cairo calling for Morsi's reinstatement and denouncing the army general who led his overthrow.
Marchers chanted "Morsi, Morsi" and "We are not terrorists", and waved picture of the ousted leader.
The protest showed tension is still running dangerously high in Egypt despite the mediation effort by the United States, the European Union, Qatar and the United Arab Emirates.
Morsi became Egypt's first freely-elected president in June 2012, 16 months after the overthrow of U.S.-backed strongman Hosni Mubarak, who had ruled for nearly 30 years.
But fears that he was trying to establish an Islamist autocracy coupled with a failure to ease economic hardships afflicting most of Egypt's 84 million people led to huge street demonstrations, triggering the army move.
Speaking about the talks in recent days, Haddad said the envoys "still carry the position that we should swallow the reality and accept that the military coup has happened and try to recover with minimum damage."
"We refuse to do so," Haddad told Reuters.
There was no agreement on how to start talks, he added.
The state news agency said earlier that diplomats, including U.S. Deputy Secretary of State William Burns and European Union envoy Bernardino Leon, had met Shater after midnight at the Tora Prison where he is being held south of Cairo.
Shater is seen as the political strategist of the group that propelled Morsi to office last year, and was arrested on charges of inciting violence after Morsi's downfall.
He told the envoys that only Morsi could "solve the mess" and the only solution was "full restoration of constitutional legitimacy and reversal of the coup", Haddad said.
"They invited him for discussions but he ended it abruptly...then he walked out of the room," Haddad said.
Morsi is being held at an undisclosed location and facing an investigation into accusations including murder. Most of the rest of the Brotherhood's leadership is also in custody.
In another development, a senior military source said the army and interim government would offer to free some Muslim Brotherhood members from jail if they had not been involved in violence.
It would allow the Brotherhood to reopen offices that had been shut after Morsi's overthrow and permit it to legalize its position to run in new elections. It would also unfreeze the group's assets and give it three ministerial posts.
"The initiative will be made so that we can end the crisis and have the Brotherhood end their sit-ins," the military source told Reuters.
A political source familiar with the proposal confirmed the details. The military source also said the government and the military had not yet agreed on Morsi's fate.
"We want the legal process to take its course while the government is seeking for all charges against him to be dropped," he said.
VIOLENCE ON HOLD
The diplomatic push has so far helped to hold off further bloodshed between Morsi's backers and the security forces.
An EU source in Brussels said the mediators were still trying to build confidence between the various sides and did not want to raise expectations.
"The real thing at this stage is to bring people together so they can actually meet and discuss these issues and for that you have to build up some trust and that can be done by very concrete measures, releasing people, dropping charges, not pressing charges, not moving into the squares, lowering the tension," the source said.
Thousands of Morsi supporters remain camped out in two Cairo sit-ins, which the government has declared a threat to national security and pledged to disperse. The interim government said on Sunday it would give mediation a chance but warned that time was limited.
Almost 300 people have been killed in political violence since Morsi's overthrow, including 80 shot dead by security forces in a single incident on July 27.
During Monday's march, protesters sprayed graffiti on walls and statues calling army chief General Abdel Fattah al-Sisi, who led Morsi's overthrow, a murderer and a traitor.
Security forces made no attempt to disperse a crowd estimated by reporters at several thousand strong.
"The military came and stole our country, they stole everything," said Mahmoud Isuafi, a businessman from the Nile Delta city of Mansoura. "I want democracy. Where is my vote? I can no longer elect my leader so I protest instead."
The military has laid out a plan that could see a new head of state elected in roughly nine months. The Brotherhood, which spent decades in the shadows before Mubarak's downfall, says it wants nothing to do with it.
However, diplomats say the Brotherhood knows Morsi will not return as president and wants a face-saving formula for him to step down that guarantees it a stake in the political future.
Two U.S. senators, Republicans Lindsey Graham and John McCain, were also due in Cairo at President Barack Obama's request to meet members of the new government and the opposition.
Before leaving on the mission, Graham said the Egyptian military must back out of politics quickly or risk a cut of the $1.5 billion in aid it receives from Washington each year.