Egypt was plunged into a political crisis following the military's overthrow of Mr Morsi more than three weeks ago.
Now supporters of the deposed leader have rejected efforts by the European Union's top diplomat to defuse the political standoff between Mr Morsi and those who ousted him.
The European Union's foreign policy chief, Catherine Ashton, became the first foreign official to see Mr Morsi since he was deposed by the army and taken into detention.
The ousted leader was detained on July the 3rd and has been placed under investigation on charges including murder.
Egypt's interim rulers flew Baroness Ashton after dark to a secret detention facility where Mr Morsi is being held.
Speaking shortly after the meeting, Baroness Ashton revealed little about the two-hour conversation with the deposed president.
"We had a warm discussion, because as you know I've met with him many times before. I sent him good wishes from people here and he asked me to pass on wishes back and of course I have tried to make sure that his family know."
Baroness Ashton's trip to Egypt is her second in just 12 days and she says meeting Mr Morsi was a condition for her return.
She earlier held talks with the interim leadership, including army chief General Abdul Fattah al-Sisi and representatives of Mr Morsi's Muslim Brotherhood.
Ms Ashton called on Egypt's leaders to be more inclusive in finding a solution to the turmoil.
"And the challenge really is to find the way in which you can bring people together and go forward bearing in mind the starting points are far apart. This is what leadership is about, this is what in a sense the challenge is for all of those who are privileged to play a leadership role in any aspect of political life."
The fate of Mr Morsi, and a deadly response from security forces on his supporters, has raised concerns about a possible bid to crush Mr Morsi's Muslim Brotherhood.
The Brotherhood won power in Egypt's elections after the 2011 uprising against former dictator Hosni Mubarak.
Despite the mediation talks, the country's crisis appears no closer to a resolution after Mr Morsi's allies revealed they are planning a major protest in Cairo.
The interim government has warned that any violation of the law will be dealt with firmly.
Senior Muslim Brotherhood member Essam El-Erian says he expects more protests throughout the country, as they would not back down until Mr Morsi is reinstated.
"The issue is not the Muslim Brotherhood against anything. The issue is that the nation, the majority of Egyptians, is pro-democracy, and anti- military coup. And when they are thinking that way, that they can end by force, any demonstration or any sit-in in any square, they are making more bloodshed not ending the protest. The protest will continue, because the protest now, and sit-in, is not here, it is in everywhere in this country in Egypt."
Egypt's interim government refuses to allow Mr Morsi to take any role in ending the turmoil gripping the north African country.
However, interim Vice President Mohammed ElBaradei says the Muslim Brotherhood should take part in the political process.
"After the 30th of June, after the uprising of the 30th of June, it was clear that there is a new phase. There was a correction of the revolution of the 21st of January, I think there is a new road map. Mr. Morsi failed, but the Brotherhood very much continues to be part of the political process and we would like them to continue to be part of the political process."
Nearly 300 people have been killed in violence since the military coup that overthrow Mr Morsi.
That includes 80 of his supporters, killed at dawn on Saturday as they marched from a month long vigil at a mosque in northern Cairo.
Egypt's authorities say Mr Morsi is being investigated on accusations including murder, stemming from a 2011 jailbreak when he escaped detention during protests against former leader Hosni Mubarak.
The Brotherhood has rejected the accusations, which also include Mr Morsi allegedly conspiring with the Palestinian group Hamas, saying they are an attempt to justify his detention.
He has not been officially charged.
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