In the latest violence, militants in the restive Sinai killed two soldiers and a policeman. Supporters of ousted Islamist president Mohamed Morsi, meanwhile, called for fresh rallies at foreign embassies in Cairo.
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 in the capital by pro- and anti-Morsi demonstrators, some of which have led to deadly clashes.
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 security forces since Morsi's ouster.
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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, told reporters that the body would accept suggestions for amendments from all groups and political parties for the next week.
Interim president Adly Mansour appointed the constitutional committee yesterday.
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 boosting the new regime's foreign relations.