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Egypt's military chief has said that economic, political and social challenges are "a real threat to the security of Egypt and the cohesiveness of the Egyptian state."
Overnight, protesters defied a curfew imposed by President Mohamed Mursi on three Suez Canal cities, attacking police stations.
There were protests after Mursi declared a 30-day state of emergency on Sunday, following a fresh wave of violence over the last week.
General al-Sisi claimed, in comments posted on the army's official Facebook page, that the army would remain "the solid and cohesive block" on which the state rests.
The military assumed power from deposed President Hosni Mubarak at the height of the uprising against him in 2011 before leading the state through an interim period that formally ended with Mursi's election in June last year.
The head of the Egyptian military has warned that political conflict in the country could lead to the collapse of the state.
General Abdel Fattah al-Sisi, who is also Egypt's defence minister, warned: "The continuation of the struggle of the different political forces ... over the management of state affairs could lead to the collapse of the state."
He also said that protecting the Suez Canal - a vital shipping route - was one of the main aims of the army deployment in the cities shaken by violence over the last week.
President Mohamed Mursi has declared a state of emergency and a curfew in three Suez Canal cities, after continued violence responding to the sentencing to death of 21 people for their role in deadly rioting at a football stadium in Port Said last February.
Seven people were shot dead and hundreds were injured in Port Said on Sunday, reports Reuters.
The shootings happened during the funerals of 33 people killed in the city when residents went on the rampage after a court sentenced 21 people to death for their role in deadly soccer violence at a stadium there last year.
Khaled Dawoud, spokesman for the National Salvation Front, Egypt's main opposition coalition, told Reuters that he welcomed steps by Mursi today to restore security in the nation.
President Mohamed Mursi has invited supporters and opponents to meet tomorrow at 6:00pm (1600 GMT) at the presidential palace in Cairo.
A statement from the presidency said it was inviting a range of Islamist allies and liberal and other opposition groups, as well as leading politicians such as leftist firebrand Hamdeen Sabahy and former foreign minister and Arab League chief Amr Moussa.
Mursi declared a state of emergency in the three most volatile cities on the Suez Canal today after waves of violence left 45 dead and hundreds injured.
Around 200 people are protesting against the Egyptian president in the city of Ismailia after he declared a state of emergency.
People marched on Sunday in the streets of Ismailia, east of Egypt's capital, shortly after President Mohamed Mursi declared a state of emergency there and in two other Suez Canal cities, a witness reported.
"Down with Mursi, down with the state of emergency," they chanted. Rights activists say the state of emergency will give police, working under the Interior Ministry, broad powers to detain people deemed a threat to security.
Egyptian president Mohamed Mursi has declared a 30-day state of emergency and a curfew in three Suez Canal cities.
He also called for dialogue with political forces to resolve the country's latest crisis, which has seen 45 people killed in violent scenes this weekend.
He said a curfew would be introduced in Port Said, Ismailia and Suez starting on Monday from 9:00pm (1900 GMT) to 6:00am (0400 GMT).
Port Said's head of hospitals, Abdel Rahman Farag, told Reuters an 18-year-old man and three other people died from gunshot wounds on Sunday.
More than 429 people suffered from teargas inhalation, while 38 were wounded by gunshots, he said.
Egypt's president, Mohamed Mursi, will address the nation this evening about the current crisis that has left more than 30 people dead and hundreds injured.
Officials said three people have been shot dead in Egypt's port city during the funerals of 33 protesters killed in a wave of violence on Saturday.
An 18-year-old man was the first confirmed victim of Sunday's violence and Abdel Rahman Farag, Port Said's head of hospitals, told Reuters that a further two other people were killed by gunshot wounds.
More than 416 people suffered from teargas inhalation, while 17 sustained gunshot wounds, he added.
More than 30 people people were killed yesterday - mostly by gunshots - when residents went on the rampage after a court sentenced 21 people to death for their role in deadly soccer violence at a stadium there last year.
Latest ITV News reports
Wherever there is division in Egypt right now – death seems sure to follow. The greatest toll came amid gunfire and tear gas in Port Said.
Riots sparked by death sentences passed in connection with last year's deadly riot at the Port Said football stadium have killed 22 people.