Ashton on Monday (29 July) became the first outsider to see Morsi since he was deposed by the army on 3 July, 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 Morsi'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 had 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 Morsi 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 León would travel to Cairo on Wednesday to "continue the work."
Nearly 300 people have been killed in violence since Morsi 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.
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 Morsi would not be part of it.
"No," interim Vice President Mohamed ElBaradei told a joint news conference with Ashton when asked whether Morsi could be part of a future process of negotiation and reconciliation.
"I think there is a new road map," ElBaradei said. "Mr Morsi 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 Morsi 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 Morsi to abandon his historic mandate as Egypt's first freely elected leader.
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 Morsi.
Meeting Morsi 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.
NATO concern for the Mediterranean region
Instability in north Africa is a concern for NATO which is keeping a close eye on events in Egypt and its neighbours, NATO's top military commander said on Tuesday.
Next to Egypt, Tunisia's moderate Islamist government is resisting opposition calls to quit and violence is on the increase in Libya.
US Air Force General Philip Breedlove, who took over as NATO's Supreme Allied Commander Europe in May, said many European NATO members bordering the Mediterranean were affected by what happened in North Africa.
"Refugee flows, commerce, drugs, all kinds of things in Europe are affected by what goes on in northern Africa so any instability in northern Africa is clearly a concern of the NATO nations," he told a news conference.
"Right now, NATO is not planning for any actions in Egypt. Much like Syria, we are keeping a close eye on it, looking at how it affects our NATO partners and if we need to, we will do what we need to do to take care of our NATO partners," he said.
He said, however, that NATO had done extensive reviews of its plans to defend NATO member Turkey, where the alliance has deployed Patriot anti-missile systems to protect it against possible attack from neighbouring Syria.