More than 60 people have been killed in the unrest.
On Thursday leaders of some of the main political factions signed an agreement condemning the violence.
But youth groups later called for more rallies. They plan to gather in Tahrir Square in Cairo after Friday prayers and march on the presidential palace.
Protesters accuse Mr Morsi of imposing a new form of authoritarianism and betraying the values of their uprising two years ago.
Supporters of Mr Morsi say the opposition is trying to use the power of the street to unseat Egypt's first democratically elected leader.
'Collapse of state'
The unrest began a week ago in Cairo on the eve of the second anniversary of the 2011 revolution and has spread to several cities.
The worst of the violence has been in the Suez Canal city of Port Said, in protests sparked by death sentences handed down to 21 local people accused of participating in football riots.
On Tuesday, Egyptian army chief Gen Abdul Fattah al-Sisi warned that the political crisis could lead to the collapse of the state.
Thursday's meeting at the al-Azhar mosque was attended by President Morsi's Muslim Brotherhood and by opposition figures.
The document signed by the leaders refers to the "sanctity of [citizens'] blood and of public and private property", according to a text published by the Egyptian al-Ahram newspaper.
It says those signing "condemn the inciting of violence, its justification... and its exploitation in any form".
Opposition politician Mohamed ElBaradei said he was optimistic after the meeting, saying differences should be solved peacefully.
Earlier this week, the National Salvation Front, formed by Mr ElBaradei, leftist Hamdeen Sabahi and former Foreign Minister Amr Moussa, turned down an invitation to talks with Mr Morsi.
They said they first wanted him to commit to the idea of a national unity government and a body to look at amendments to the new Egyptian constitution.
