President Mohamed Mursi is inviting political groups in Egypt to take part in a national dialogue on a political roadmap after a referendum on a new constitution.
Clashes between opponents and supporters of Mr Mursi earlier left five people dead and 644 injured.
He has asked heads of political parties, revolutionary youth and senior legal figures to meet at the Presidential place on Saturday.
In a televised address on Thursday night, Mr Mursi called for the country's political differences to be decided by dialogue, and not by violence.
He said the meeting would also discuss the fate of the upper house of parliament after the lower house was dissolved in June.
He added that he supported the right to peaceful protest but said that some people had been paid to foment violence.
Mr Mursi said that 80 people had been detained as they had been "implicated in violent acts".
The president 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.
Tanks and armoured troop carriers are deployed outside the presidential palace in Cairo after clashes between supporters and opponents of President Mohammed Mursi.
The streets of the capital are now reported to be calm. Most people had left the area before a deadline of 3pm on Thursday.
Earlier, five people died and 644 were injured in overnight clashes between the president's supporters and his opponents.
Tanks and armoured troop carriers were deployed outside the presidential palace on Thursday morning.
Major General Mohammed Zak, the head of the Republican Guard, said they had been sent there to separate the rival protesters.
The president adopted new powers in a decree on 22 November and stripped the judiciary of any power to challenge his decisions. Mr Mursi says he will give up his new powers once a new constitution is ratified.
The BBC reports Mr Mursi is expected to address the nation later on Thursday.
Four of his advisers resigned on Wednesday. Three others did so last week and the Mena news agency reported a further resignation on Thursday.