Morsi precipitated immediate accusations of Mubarak-style dictatorship, spurring secular oppositionists to form the National Salvation Front.
Egypt's main opposition coalition, the National Salvation Front, said it would meet on Monday morning to discuss the initiative.
The Al-Yawm al-Sabi website carried criticism by the opposition National Salvation Front.
He said he expected other groups in the opposition National Salvation Front (NSF) coalition to follow suit with a boycott when they meet on Tuesday.
In 1989, Romania's National Salvation Front named a new government headed by President Ion Iliescu, a day after announcing the execution of deposed dictator Nicolae Ceausescu.
It is also been noted that there is no sign in Algiers of the previously well organised Islamic Salvation Front sending in its own volunteers to help out.
Mr Maati rejected opposition allegations that fake judges supervised some of the polling - one of several complaints relating to voting fraud made by the opposition National Salvation Front after each stage of voting.
Mohamed ElBaradei, a leading member of the opposition National Salvation Front, told journalists that before it would attend any national dialogue, the president would have to appoint a national unity government and take steps to amend the disputed constitution.
But Mohamed ElBaradei, head of the Constitution Party and a member of the National Salvation Front, reiterated two demands before the front would engage in dialogue: the formation of a new government and a committee to amend the constitution.
It is far too early to say whether the fractious Egyptian opposition that has just begun to coalesce under the banner of the National Salvation Front will be able to pose a real challenge to the Muslim Brotherhood and other Salafists.
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