Mursi's decision on Saturday to retract a decree awarding himself wide powers failed to placate opponents who accused him of plunging Egypt deeper into crisis by refusing to postpone the vote on a constitution shaped by Islamists.
"We are against this process from start to finish," Hussein Abdel Ghani, spokesman of the National Salvation Front, told a news conference, calling for more street protests on Tuesday.
The Front's main leaders - Nobel peace laureate Mohamed ElBaradei, former Foreign Minister Amr Moussa and leftist Hamdeen Sabahy - did not attend the event.
Hundreds of protesters milled around Mursi's palace, despite tanks, barbed wire and other barriers installed last week after clashes between Islamists and their rivals killed seven people.
"Holding a referendum now in the absence of security reflects haste and an absence of a sense of responsibility on the part of the regime, which risks pushing the country towards violent confrontation," a statement from the Front said.
The Muslim Brotherhood, which propelled Mursi from obscurity to power, urged the opposition to accept the referendum's verdict.
Islamists say the vote will seal a democratic transition that began when a popular uprising toppled Hosni Mubarak 22 months ago after three decades of military-backed one-man rule.
Their liberal, leftist and Christian adversaries say the document being fast-tracked through could threaten freedoms and fails to embrace the diversity of Egypt's 83 million people.
"Act of war"
Mursi had given some ground on Saturday when he annulled the fiercely contested decree issued on November 22 that gave him extra powers and shielded his decisions from judicial review.
But some measures taken under the decree remain in force and the president has insisted the referendum go ahead on December 15.
Liberal opposition leader Ahmed Said earlier described the race to a referendum as an "act of war" against Egyptians.
Egypt is torn between Islamists, who were suppressed for decades, and their rivals, who fear religious conservatives want to squeeze out other voices and restrict social freedoms. Many Egyptians just crave stability and economic recovery.
Brotherhood spokesman Mahmoud Ghozlan said the scrapping of Mursi's decree had removed any reason for controversy.
"We ask others to announce their acceptance of the referendum result," he said on the group's Facebook page, asking whether the opposition would accept "the basics of democracy".
The cancellation of Mursi's decree, announced after a "national dialogue" on Saturday boycotted by almost all the president's critics, has not bridged a deep political divide.
Prime Minister Hisham Kandil, a technocrat with Islamist leanings, said the referendum was the best test of opinion.
"The people are the makers of the future as long as they have the freedom to resort to the ballot box in a democratic, free and fair vote," he said in a cabinet statement.
But opposition factions, uncertain of their ability to vote down the constitution against the Islamists' organisational muscle, want the document redrafted before any vote.
"A constitution without consensus can't go to a referendum," said Hermes Fawzi, 28, a protester outside the palace. "It's not logical that just one part of society makes the constitution."
Egypt tipped into turmoil after Mursi grabbed powers to stop any court action aimed at hindering the transition. An assembly led by the Brotherhood and other Islamists then swiftly approved the constitution it had spent six months drafting.
Opponents, including minority Christians, had already quit the assembly in dismay, saying their voices were being ignored.
After the dialogue hosted by Mursi, a spokesman announced that the president had issued a new decree whose first article "cancels the constitutional declaration" of November 22. He said the referendum could not be delayed for legal reasons.
The decree ignited more than two weeks of sometimes violent protests and counter-rallies in Egypt. Mursi's foes have chanted for his downfall. Islamists fear a plot to oust the most populous Arab nation's first freely-elected leader.
Islamists reckon they can win the referendum and, once the new constitution is in place, a parliamentary election about two months later. The Islamist-led lower house elected this year was dissolved after a few months by a court order.
Investors appeared relieved after Mursi rescinded his decree, sending Egyptian stocks 4.4 percent higher on Sunday. Markets are awaiting approval of a $4.8 billion IMF loan later this month designed to support the budget and economic reforms.
The military, which led Egypt's transition for 16 turbulent months after Mubarak fell, told feuding factions on Saturday that only dialogue could avert "catastrophe". But a military source said these remarks did not herald an army takeover.
© Thomson Reuters 2012