He also denounced as illegitimate the court that is trying him on charges of inciting murder and violence.
Mr Morsi refused to name any lawyers to defend him in the trial, which has been adjourned until 8 January.
He is one of thousands of Muslim Brotherhood members to have been detained over the past four months in a crackdown the interim authorities have portrayed as a struggle against “terrorism”.
Hundreds of people have also been killed in clashes with security forces.
On Monday, the government said it would be lifting the state of emergency and curfew imposed in August to limit protests.
However, security will be bolstered in city centres and on main roads, and activists expect the introduction of a new law giving police the power to ban demonstrations outright.
Mr Morsi was moved to a regular prison last week after the first session of his trial on charges of incitement, in connection with the violence outside the Ittihadiya presidential palace in Cairo in December 2012.
At a meeting with a team of lawyers from the Brotherhood and other allied groups on Tuesday, he dictated a “message to the Egyptian people”.
“The coup has begun to fall apart and will topple in the face of the steadfastness of the Egyptian people,” the lawyers quoted the statement as saying on Wednesday.
Mr Morsi accused armed forces chief Gen Abdul Fattah al-Sisi, who announced the overthrow of the president following days of mass opposition protests, of “treason against God” and “treason against the whole nation by driving a wedge among the people of Egypt”.
Egypt would not regain its stability until “the military coup is eliminated and those responsible for shedding Egyptians’ blood are held accountable”, he warned.
Brotherhood lawyer Mohammed al-Damati said Mr Morsi was still refusing to accept legal representation for his trial, insisting it was illegitimate.
“When we discussed the issue of naming a lawyer to defend him, he said that the time was too early to talk about this because he adheres to his legitimacy.”
However, the lawyers would initiate “legal measures against the coup”, Mr Damati said. These might include complaining to the prosecutor general that “what happened was a crime”, or filing a suit at an administrative court alleging that Gen Sisi’s moves were “null and void”, he added.
Later, state-run Nile News TV reported that the Misdemeanour Court in Burj al-Arab, in Alexandria, had ruled that the separate trial of Mr Morsi on fraud charges would begin on 23 December.
The charges were connected with the Muslim Brotherhood’s economic and social programme for Egypt’s recovery, called Renaissance (al-Nahda), it said.
Supporters claim both the incitement and fraud charges are politically motivated, something the military backed government denies.