It replaces the constitution drafted by an Islamist-led panel, approved in a referendum last year, and suspended after Morsi's ouster.
The Islamist-drafted charter had galvanized opposition against Morsi, amid a last minute walk-out from the secular and Christian members of the 100-panel member, appointed then by the Islamist-dominated parliament.
Opponents were protesting the charter because they said it had an Islamist slant, giving religious interpretations a greater role in legislation and trampling on rights and freedoms.
Despite a 63 percent approval, turnout was low, a little more than 30 percent— and many of Morsi's opponents used the disputed constitution as a rallying point to campaign against him.
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A bigger margin and stronger turnout now could be touted as a show of the legitimacy of the post-coup leadership, particularly amid continued opposition from Morsi supporters to the road map and the current authorities.
The referendum on the constitution sets in motion a schedule for parliamentary and presidential elections to replace the interim authorities with a newly elected government and legislature.
State television has already launched a campaign calling on Egyptians to vote yes in the referendum. Billboards are up around Cairo, urging voters to take part in the referendum as a sign of support for post-Morsi arrangements.
"After we wasted a long time, that passed slowly, heavily and harshly on many of Egypt's poor, it is time we complete our revolution and rebuild this nation to realize the popular aspirations and ambitions," Mansour said in a televised speech.
Mansour said the amended charter upholds freedoms and rights, establishes the separation of powers, and respects Egyptians' moderate religious beliefs. He appealed to opponents of the documents, and in clear reference to supporters of Morsi, to end their "stubbornness," stop "chasing illusions" and accept the transition plan.
Morsi supporters, largely Islamist groups led by the Muslim Brotherhood, have held near daily protests calling for Morsi's reinstatement and a return to the 2012 constitution. It is likely that they will boycott the upcoming referendum, although a formal announcement is expected this week.
"We are heading toward a boycott campaign," said Islam Tawfiq, a member of the Muslim Brotherhood's political party. "Participating in the referendum, even with a no vote, would be an implicit recognition of the legitimacy of the (military-backed) road map."
Some Islamists however are rallying behind the new referendum. The ultraconservative Salafist Al-Nour party, the only Islamist party who took part in the drafting process, is campaigning for a yes vote, inviting harsh criticism from Morsi allies— some of whom portray the new document as anti-Islamic.
The adoption of the constitution is vital for the country's current authorities as it could be interpreted as a sign of renewed popular support as voices of dissent have begun to rise even among secular, anti-Morsi forces.
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Gamal Eid, head of the Arab Network for Human Rights Information that is currently carrying out a detailed study of the amended charter, said he will recommend a "no" vote.
He said nearly 30 articles in the 247-article draft charter are too vague— giving authorities room to stifle freedom of association and information, for instance. He also said other articles give the military powers that are too wide, "making it a state above the state."
He was referring to articles that give the military the right to appoint the defense minister for at least eight years during a transitional period, and the right to try civilians in military trials for any offense involving a military person or those under its authority.
"Why vote yes to a constitution that we think has many problems?" Eid said.
Sally Toma, a leading activist who took part in the January 2011 uprising against longtime autocrat Hosni Mubarak, and who was critical of Morsi, also disproves of the military-backed authorities, saying their new document falls short of her expectations.
She said the amended charter didn't commit to a process of transitional justice that would hold accountable security and military officials for the killing and torturing of protesters in recent years of turmoil.
"There should be accountability, there is no revolution without transitional justice," Toma said, adding that a protest will be held on Monday in commemoration of the dispersal by security forces of a sit-in organized in 2011 that left at least 17 dead.