|Riot police beat an anti-Mursi protester during clashes along Qasr Al Nil bridge in Cairo, on Monday.|
Egypt's main opposition alliance has rejected the president's call for national dialogue as empty of content.
Mohammed Morsi had urged opposition leaders to attend a meeting following four days of deadly violence.
Dozens have died since a court sentenced 21 people to death over football riots last year. Anger over Mr Morsi's rule has fuelled other unrest.
A state of emergency has been declared in Port Said, Suez and Ismailia, and a night-time curfew will begin later.
The violence continued on Monday morning, with one man killed by gunfire near Cairo's Tahrir Square.
Also on Monday, the cabinet approved a draft law allowing the army to participate in policing and have the power of arrest.
Mohamed ElBaradei, a leading member of the opposition National Salvation Front, told journalists that before it would attend any national dialogue, Mr Morsi would have to appoint a national unity government and take steps to amend the disputed constitution.
"The dialogue to which the president invited us is to do with form and not content," Mr ElBaradei said.
"We support any dialogue if it has a clear agenda that can shepherd the nation to the shores of safety."
Former presidential candidate Hamdeen Sabahi, speaking at the same news conference, said: "We aspire to a dialogue, but there are no guarantees that this dialogue will be a success... while blood is being spilled."
Mr Morsi had called the meeting for 18:00 local time (16:00 GMT).
The BBC's Yolande Knell, in Cairo, says the president had been hoping that dialogue could restore national unity amid growing concern about the scale of the latest unrest.
He invited representatives from 11 political forces - Islamists, liberals and leftists - to come to the presidential palace for talks, but so far it is unclear who will accept his invitation, our correspondent adds.
The opposition accuses Mr Morsi of being autocratic and driving through a new constitution that does not protect adequately freedom of expression or religion.
The constitution was approved in a national referendum in December.
Another anti-Morsi rally is scheduled for Cairo for Monday afternoon.
Mr Morsi announced the state of emergency in Port Said, Suez and Ismailia in a national televised address on Sunday evening.
He said he might take further steps "for the sake of Egypt", as it was his "duty" as president.
"I have said I am against any emergency measures but I have said that if I must stop bloodshed and protect the people, then I will act," the president added.
"If I must, I will do much more for the sake of Egypt. This is my duty and I will not hesitate."
The draft law passed by the cabinet on Monday allowed the army "to participate with the police in preserving security and protecting vital establishments", state news agency Mena said. Those arrested by the army would by tried by a civilian court if charged, it added.
Violence continued overnight, with anti-Morsi protesters in Ismailia clashing with police, who responded with tear gas.
About 30 people died in unrest in Port Said on Saturday, while another three were killed at a mass funeral on Sunday.
The protests began in Port Said after a court sentenced 21 local people to death over riots that killed 74 people after a football game last February.
February's riots began when fans of Port Said side al-Masry attacked visiting supporters from Cairo club al-Ahly. Fans flooded on to the pitch, attacking al-Ahly players and fans as the match ended. Most of the victims died of concussion, cuts and suffocation.
Early on Monday, protesters and riot police also clashed for a fifth consecutive day in Cairo, where the anger focuses more heavily on the constitution and on what Mr Morsi's opponents say is a betrayal of the revolution that overthrew Hosni Mubarak.
Protests last week marking the second anniversary of the uprising left five people dead in Suez.