Egypt's new cabinet has held its first meeting and urged all parties to keep their demonstrations peaceful, as a panel named to amend the constitution has called on all sides to contribute to its deliberations.
In the latest violence, fighters in the Sinai killed two soldiers and a policeman on Sunday.
Unidentified gunmen shot dead the three members of the security forces in the town of El-Arish in separate attacks, in the Sinai region that has seen regular attacks on security forces since Morsi's ouster.
The unidentified assailants shot dead one soldier in front of the television and broadcasting building and another who was on guard duty, and killed the policeman in an attack on a police station, a security source said.
Forging ahead with an army "roadmap" for political transition, meanwhile, Foreign Minister Nabil Fahmy launched a public relations campaign to boost the army-backed administration's credibility abroad.
The caretaker cabinet, in a meeting chaired by prime minister Hazem Beblawi, urged "all political parties to express their opinions peacefully, and to renounce violence", after weeks of mass protests in the capital by pro- and anti- Mohamed Morsi demonstrators, some of which have led to deadly clashes.
The meeting focused on Egypt's battered economy and the security situation.
A newly appointed panel of four university professors and six judges also held talks on drafting a new constitution at the Shura Council, or upper house of parliament, the official MENA news agency said.
The head of the panel, the president's legal adviser Ali Awad Saleh, told reporters that the body would accept suggestions for amendments from all groups and political parties for the next week.
At its first meeting on Sunday, the new cabinet called on "all political parties to pursue the peaceful expression of their views, and to renounce violence".
Meanwhile, a few thousand women, children and men marched from the site of a round-the-clock, pro-Morsi vigil in a Cairo suburb on Sunday to protest the deaths of three women who were killed in a protest on Saturday.
"Why, Sisi why, why did you kill our sisters?" the crowd chanted, referring to General Abdel Fattah al-Sisi, the defence minister who played a central role in forcing Morsi from office following mammoth street protests against the leader.
Supporters of Morsi, who was ousted after a single turbulent year of rule, have pressed demonstrations, holding marches and protests across the country since his fall.
Thousands of Morsi loyalists have been massed in Cairo's Rabaa al-Adawiya square for about three weeks, demanding his reinstatement and denouncing General Abdel Fattah al-Sisi, the army chief behind his overthrow.
In addition to the demonstration in Cairo, pro-Morsi protesters also held gatherings in Suez, Alexandria, Fayoum, Minya, Bani Suef, Mansoura, El-Arish and Ismailia.
At least 22 people were injured in Suez after clashes broke out between protesters and area residents.