The Muslim Brotherhood has said it proposed a framework for talks to resolve Egypt's political crisis, its first formal announcement of an offer for negotiations since President Mohammed Mursi was toppled.
Brotherhood official Gehad el-Haddad, who represented the movement in previous EU-facilitated talks, said the proposal had been made to EU envoy to the region Bernardino Leon before a visit on Wednesday by EU foreign affairs chief Catherine Ashton.
Mr Leon confirmed he had offered the European Union's "good offices" to help resolve the crisis, although he said the term "mediator" exaggerated the role.
The proposal, as described by Mr Haddad, was still in its early stages. He did not give details, described it as only a "framework" for opening a channel of dialogue, and insisted on the Brotherhood's firm demand that the July 3 "coup" that brought down Mr Mursi be reversed.
He also said it was not clear who would represent the opposite side: the military which removed Mr Mursi or politicians.
"We need a third side. It's not even clear who the third side would be. Is it the army? The NSF?" he said, referring to the National Salvation Front made up of political groups that oppose Mr Mursi.
Mr Leon, who spoke by telephone on board his flight back to Brussels from Cairo, declined to go into details of any proposals he had received but said he believed the sides were growing more open to talks.
"It is too early to talk about initiatives. We have just listened to the parties and to their positions and any possible room for openness to support. We believe that this should be an Egyptian dialogue and no foreign actors," Mr Bernadino said.
During her visit on Wednesday, Ms Ashton met several senior Brotherhood figures as well as the interim authorities. The visit provided a notable contrast with one two days earlier by a senior U.S. envoy, who left without meeting the Brotherhood.
An aide to Mohamed ElBaradei, the NSF leader named vice president in the interim government, had no immediate comment to make.
Mr Haddad said the Brotherhood would be willing to negotiate over any political issue, including new elections to replace Mr Mursi as president, but insisted that the army would first have to reverse its decree that unilaterally removed Mr Mursi.
"First they have to reverse the coup," he said. "You can't come in on a tank and remove an elected leader. It is a stand-off, it is either a military coup or a democratic choice," he said in a midnight interview at site in Cairo of a mass vigil by thousands of protesters demanding Mr Mursi's return.
Mr Leon acknowledged that the sides were far apart.
"They are both in very firm positions, but at the same time we think that they are not completely closed to the possibility of re-engaging. So, I wouldn't say that we left Egypt optimistic, but at least I can say not pessimistic either."
Mr Mursi and a small number other Brotherhood figures - including Mr Haddad's father - have been held by the armed forces at an undisclosed location since he was toppled.
The Brotherhood has maintained its vigil near a Cairo mosque into its third week. Since Mr Mursi's fall, protest marches have frequently led to violence in which at least 99 people have been killed, with both sides blaming the other.
Hundreds of supporters of Mr Mursi have been rounded up and the authorities have issued arrest warrants for most of the group's leaders. Mr Haddad himself said he faced treason charges.
The interim government has invited the Brotherhood to participate in the transition leading to new elections, expected in about six months. The Brotherhood has dismissed those offers as propaganda.
Mr Haddad said the authorities were determined to destroy the Islamist organisation to ensure it never won elections again, a policy he said would backfire by pushing the Brotherhood underground where it survived during decades of military rule.
"They need to give the Brotherhood deep enough blows that it won't be able to contest anything new. How do they do that? Freezing the assets, arresting the top leaders, closing down the party and the Brotherhood headquarters and offices across the country, and killing people on the street," he said.
"And they think we are going to budge? This is an organisation built for 86 years under oppressive regimes. That is the nature of the organisation; that is our comfort zone. They just pushed us back into it."
Mr Haddad said the Brotherhood could participate in new elections but that it would be unlikely to accept them as long as the military had shown it was willing to overrule the result.
"Either we force the military's head back into the barracks, and they have to be taught a lesson not to pop their head back into the political scene ever again, or we die trying," he said.
Spaniard Mr Leon acted as a go-between in secret negotiations in the first half of this year between the Brotherhood and the NSF. The Brotherhood was represented by Mr Haddad and the NSF by figures including Mr ElBaradei.
Those discussions, failed to produce a deal in time to save Egypt's first freely elected president. But they did establish the EU as a trusted neutral party at a time when Washington is doubted by both sides.
According to Mr Haddad's account, largely matching the accounts from EU and NSF figures, the sides were close to agreement on three main opposition demands: a new cabinet, revisions to an electoral law and the removal of the public prosecutor.
Mr Haddad said the main disagreement ended up being the fate of Hisham Kandil, Mr Mursi's prime minister. The Brotherhood had been willing to let the opposition name a replacement, but Mr Mursi refused, arguing that the prime minister needed to come from a party with strong representation in parliament, Mr Haddad said.
However, he also said the NSF figures on the opposite side seemed determined to avoid reaching a deal no matter what.
"If the NSF were to send the president a list of their demands, literally everything they could think of, on NSF letterheaded paper, and the president were to remove the NSF letterhead and put it on a presidential letterhead, and sign it and seal with with a presidential seal, and issue it as a decree - they would go to the street protesting against it."