Lawmaker Mustafa Bakri outlined the ultimatum after representatives of 18 parties and independent lawmakers met with the head of the council, Field Marshal Hussein Tantawi.
Party representatives announced that, if parliament failed to agree to issue viable membership criteria by Thursday, the SCAF would unilaterally issue a 'constitutional annex' or revive Egypt's 1971 constitution, suspended since last year's Tahrir Square uprising.
Several parties, including the Muslim Brotherhood's FJP, the Egyptian Social Democratic Party, headed by Mohamed Abul-Ghar, and the moderate-Islamist Wasat Party, headed by Abu-Ela Madi, refrained from attending the meeting. Members of parties that did attend the meetings, said that there will be negotiations soon between those who attended and those who did not, in order to see if agreement can be reached regarding the criteria for the Constituent Assembly. Parliament formed an Assembly in April, but soon after its formation it became defunct as most members of other parties than the Muslim Brotherhood and the Salafists withdrew in protest against the heavy over representation of Islamists.