Cairo (CNN) -- Opponents of Egyptian President Mohamed Morsy's upcoming constitutional referendum called Sunday for new nationwide protests.
Emerging from a meeting attended by key opposition leaders in Cairo, a spokesman for the National Salvation Front, a coalition of opposition organizations, said protesters are planning a massive rally Tuesday.
There were scattered anti-Morsy demonstrations Sunday as a heavy security presence surrounded the presidential palace along concrete walls installed around the building.
The call for demonstrations follows news that Morsy refused to delay a Saturday vote on a new constitution even as he rolled back a controversial edict that gave himself sweeping powers.
The move was an attempt to stamp out a political crisis that has spilled into the streets, pitting the president's supporters and opponents against one another and raising questions about Morsy's ability to lead the fragile democracy.
Almost as soon as Morsy adviser Mohamed Selim el-Awwa laid out the offer Saturday, many in the opposition dismissed it.
"No, there is better democracy than that," Amr Moussa, former head of the Arab League and a key opposition figure, told CNN.
"If the constitution lacks serenity and objectivity in certain of its articles, we have time, enough time to change those articles."
Morsy has refused to delay the referendum, saying a constitution is essential for the fledgling democracy, while the opposition says the document does not represent all Egyptians.
An independent judicial panel backed Morsy's announcement on Saturday, finding that the referendum must be carried out on December 15 to meet a legal requirement.
The presidential palace has been the seen of violent clashes pitting thousands of protesters -- for and against Morsy.
Egyptian authorities said at least six people have been killed in violent clashes in recent days, while the Muslim Brotherhood -- the group that backs Morsy -- has said eight of its members were killed.
The crisis erupted in late November when Morsy issued the edict allowing himself to run the country unchecked until a new constitution was drafted, a move that sat uncomfortably with many Egyptians who said it reminded them of ousted President Hosni Mubarak's rule.
Morsy had said the powers were necessary and temporary. But that promise did little to quiet the opposition.
Anger at Morsy's move led to protesters reoccupying Tahrir Square, the scene of the Arab Spring uprising that saw Mubarak ousted in 2011. Thousands later protested outside the palace, where the opposition clashed with the Muslim Brotherhood.
The anger only grew when the Islamist-dominated Constitutional Assembly pushed through a draft despite the objections of the secular opposition, including some members who walked out in protest.
A coalition of Egyptian Islamic parties, including the Brotherhood, rejects any postponement in the constitutional referendum, the Islamic Forces Alliance announced Saturday on the Brotherhood website.
CNN's Reza Sayah reported from Cairo, and Amir Ahmed from Atlanta. CNN's Chelsea J. Carter and Dana Ford contributed to this report.