Clashes between opponents and supporters of Mr Morsi left five people dead and 644 injured overnight.
In a televised speech, Mr Morsi expressed sorrow over the deaths.
He added that he supported the right to peaceful protest but alleged that some people had been paid to foment violence.
Mr Morsi said that 80 people had been detained as they had been “implicated in violent acts”.
He said that a controversial article in a recent declaration which gave him sweeping powers could be modified after discussions with opposition forces.
The declaration would be cancelled after a referendum on a new constitution planned for 15 December, whatever the result, Mr Morsi added.
Mr Morsi confirmed that the referendum would go ahead as planned, saying that if the constitution was voted down, another constituent assembly would be formed to write a new draft.