Senior Brotherhood leaders accuse the opposition of seeking to topple Morsi and undermine his legitimacy.
The draft charter was adopted despite a last minute walkout by liberal and Christian members of the Constituent Assembly. The document would open the door to Egypt's most extensive implementation of Islamic law or Shariah, enshrining a say for Muslim clerics in legislation, making civil rights subordinate to Shariah and broadly allowing the state to protect "ethics and morals."
It fails to outlaw gender discrimination and mainly refers to women in relation to home and family. The charter also has restrictive clauses on freedom of expression.
Khaled Dawoud, a spokesman for the National Salvation Front, said the opposition is hoping to continue its pressure to lead Morsi to reconsider holding the referendum "and give us more time to discuss a new draft."
"We will try our best so that this referendum doesn't take place," he said.
In his announcement a day earlier, Morsi replaced the scrapped decrees with a new one that doesn't give him unrestricted powers, but allows him to give voters an option if they decide to vote "no" on the disputed draft charter.
In the new decree, if the constitution is rejected, Morsi would call for new elections to select 100-member panel to write a new charter within three months. The new panel would then have up to six months to complete its task, and the president would call for a new referendum with a month.
The process would add about 10 more months to Egypt's raucous transition, but could answer some of the opposition demands of a more representative panel to write the charter, if the elections are not swept by Islamists.
The opposition has held a sit-in outside the presidential palace since Friday. A rally of a few thousand marched to join them Sunday.
In a nearby area, several hundred Morsi supporters held a rival rally, lining the street and chanting to traffic: "Islamic Islamic," saying that voting day "will bring stability."