* Ashton says Mursi well, will return to press mediation effort
* Flown by military helicopter, after dark
* Egypt rulers link dialogue to a halt to violence
* ElBaradei: No role for Mursi in negotiations
Egypt allowed Europe's top diplomat to meet deposed Islamist president Mohamed Mursi on Monday, flying her after dark to Mursi's secret detention facility but ruling out any role for him in ending the turmoil convulsing the country.
Catherine Ashton, the European Union's foreign policy chief, became the first outsider to see Mursi since he was deposed by the army on July 3, taken into detention and placed under investigation on charges including murder.
His fate - and a deadly crackdown by security forces on his supporters - has raised global anxiety about a possible bid to crush Mursi's Muslim Brotherhood, a movement that emerged from decades in the shadows to win power in elections after the 2011 uprising against Hosni Mubarak.
Ashton revealed little about what she called a "friendly, open and very frank" two-hour conversation with the deposed president. An aide said they had "in-depth" talks.
"I've tried to make sure that his family knows he is well," said Ashton, who has emerged as one of the only figures accepted by both sides as mediator in a conflict that has found the United States cast as a meddling hand.
Flown to the meeting by military helicopter, Ashton said Mursi had access to television and newspapers and was informed about the situation in the country. "I saw where he was," she said. "I don't know where he is but I saw the facilities he has."
Ashton spent Monday shuttling between Egypt's rulers and the Brotherhood to try to pull the country back from more bloodshed.
In a possible sign of progress, a spokesman for Ashton said EU envoy Bernadino Leon would travel to Cairo on Wednesday to "continue the work."
Nearly 300 people have been killed in violence since Mursi was removed, including 80 of his supporters gunned down at dawn on Saturday as they marched from a month-long vigil at a mosque in northern Cairo.
ARMY ROAD MAP
The Brotherhood vows to protest until Mursi is reinstated. It said its supporters would be on the move again on Tuesday, though twice this week it has failed to follow through on pledges to march to sensitive security facilities in Cairo.
The U.S. embassy said it was closing early on Tuesday in anticipation of marches in Cairo's diplomatic district.
The crisis has left Washington treading a fine line with a pivotal Arab ally that it funds with $1.3 billion a year in military aid and whose stability is of crucial importance to Middle East peace.
Ashton stressed the need for an "inclusive" process to ending the confrontation, one that would necessarily include the Brotherhood. But Egypt's army-installed interim government made clear Mursi would not be part of it.
"No," interim Vice President Mohamed ElBaradei told a joint news conference with Ashton when asked whether Mursi could be part of a future process of negotiation and reconciliation.
"I think there is a new road map," ElBaradei said. "Mr Mursi failed, but the Brotherhood very much continue to be part of the political process and we would like them to continue to be part of the political process."
He said an end to violence, which the government blames on its foes, would allow the shutdown of the Brotherhood's sit-in protests and create room for dialogue. The Brotherhood accuses the security forces of stirring up the violence to justify their crackdown on the Islamists.
Media have speculated about why the military-backed rulers would have allowed Ashton to meet the ousted leader, who had been kept incommunicado for a month.
She denied carrying an offer to Mursi of "safe exit" if he were to renounce his claim to the presidency.
Many people have suggested such an arrangement could be part of a deal that would allow the Brotherhood to leave the streets and join an army-backed "road map" to civilian rule, but would require Mursi to abandon his historic mandate as Egypt's first freely-elected leader.
CALL FOR RELEASE
The road map envisions parliamentary elections in about six months to be followed by presidential polls. Accusing the army of mounting a coup, the Brotherhood says it wants nothing to do with it. The army said it acted in response to mass protests last month against Mursi.
Meeting Mursi was a condition of Ashton's offer to visit Egypt, where she also met the general who removed him and other leaders on her second trip in 12 days.
Since the fall of Mubarak as the Arab Spring revolutions took hold more than two years ago, the Arab world's most populous nation has remained in turmoil, arousing concern among allies in the West and in neighbouring Israel, with which Egypt has had a peace treaty since 1979.
Egypt's authorities say Mursi is being investigated on accusations including murder, stemming from a 2011 jailbreak when he escaped detention during protests against Mubarak.
The Brotherhood says the accusations, including conspiring with the Palestinian group Hamas, are absurd and trumped up to justify his detention. He has not been officially charged.
French Foreign Minister Laurent Fabius called on Tuesday for Mursi to be released. Washington and other Western capitals have made similar calls.