Egypt's new cabinet held Sunday its first meeting and urged parties to keep their demonstrations peaceful, as a panel named to amend the constitution called on all sides to contribute.
In the latest violence, militants killed two soldiers and a policeman in the Sinai peninsula.
In Cairo hundreds of women marched to the defence ministry to protest the killing of three women on Friday at a rally in Mansura of supporters of deposed Islamist president Mohamed Morsi.
Footage broadcast on private television station ONTV showed soldiers blocking the way to the defence ministry, barring the road with barbed wire.
Morsi's Muslim Brotherhood, meanwhile, outlined plans for ending the political crisis in Egypt after nearly three weeks of protests calling for his reinstatement, insisting again on his return.
Forging ahead with an army "roadmap" for political transition, 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 by pro- and anti-Morsi demonstrators, some of which turned deadly.
The meeting focused on Egypt's battered economy and the security situation.
Unidentified gunmen shot dead the three members of the security forces in the town of El-Arish in separate attacks, in the increasingly lawless Sinai region that has seen regular attacks on police and soldiers since Morsi's ouster.
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, said the body would accept suggestions for amendments from all groups and political parties for the next week.
In the wake of the July 3 coup, Egypt's new leadership suspended the constitution that had been drawn up by an Islamist-dominated panel and adopted by referendum in December with a majority of 64 percent, but with a voter turnout of just 33 percent.
Interim president Adly Mansour appointed the constitutional committee on Saturday.
Its members have 30 days to complete their task, after which their amendments will be brought before a 50-strong body representing different groups in Egyptian society, which will submit final changes to Mansour, before he puts it to a referendum.
Work also continued on building the new regime's foreign relations.
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Fahmy said Morsi's decision to cut diplomatic ties with war-torn Syria would be "re-examined".
Morsi had repeatedly called on Syrian President Bashar al-Assad to resign.
"There is no intention of jihad in Syria," Fahmy said, referring to calls for a holy war in Syria under Morsi's presidency.
But Fahmy also met the new leader of Syria's main opposition coalition, Ahmad Jarba, on Sunday, saying that Egypt supports the Syrian people in their aspirations.
In a boost to the new administration, King Abdullah II of Jordan on Saturday became the first foreign head of state to visit since the army ousted and detained Morsi.
King Abdullah pledged his support "for Egyptian national choices", the presidency said.
But Morsi's supporters have flatly rejected the legitimacy of the interim cabinet.
On Sunday, the Muslim Brotherhood issued a statement giving their vision for an end to the political crisis, saying the solution rests in Morsi's return to office.
The Brotherhood called for the army to "respect the will of the people," by returning "constitutional legitimacy, with the constitution, the president and the parliament."
Once reinstated Morsi would carry out "the reform initiative he committed to according to the constitution decided on by the people," the statement said.
And when all these conditions are met "all national and political forces (would) meet for dialogue without a roof" on the country's future, it added.
Morsi's supporters had called for fresh rallies in the capital on Sunday, planning marches to foreign embassies in Cairo, including that of the United States.
But the US mission in Cairo's Garden City remained quiet, an AFP correspondent said and no reinforcements were called in to bolster the guards outside the embassy.
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 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.