The visit in the early hours of yesterday was the first time anyone has officially been allowed to meet the deposed leader since his July 3 ouster by the army.
It came as Morsi's supporters vowed no let-up in their demonstrations for his reinstatement despite weekend clashes that left 82 people dead.
"Morsi is well," Ashton told reporters.
"He has access to information in terms of TV, newspapers, so we were able to talk about the situation and we were able to talk about the need to move forward.
Sources told AFP that Ashton left Cairo by military helicopter to visit Morsi, who is being held on allegations related to his escape from prison during Egypt's 2011 uprising.
On her last visit on July 17, Ashton unsuccessfully requested to meet the ousted president and urged his release.
This time, meeting him was a condition of her visit to Egypt, she said.
"I said that I would not come unless I could see him and that was freely offered to me."
"We want to help facilitate the bringing together of ideas," she said, adding that she was hoping to find "common ground."
"I don't come here to say somebody should do this, somebody should do that, this is your country," she said.
On Sunday and yesterday, Ashton met army chief General Abdel Fattah al-Sisi, interim president Adly Mansour and vice president Mohamed ElBaradei, who she was due to see again later today.
She also met representatives of the pro-Morsi coalition, which confirmed that "no initiatives" to resolve the crisis had been discussed and said its position was unchanged.
"We are ready to talk to anybody, but we don't see anything positive from the other side," added Amr Darrag, a senior member of the Muslim Brotherhood's political army.
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