Mursi was due to ratify the constitution, hastily approved by an Islamist-dominated drafting assembly on Friday, later in the day and to set a date for a referendum on it within 15 days.
Tens of thousands of Egyptians protested against Mursi on Friday and rival demonstrators threw stones after dark in Alexandria and the Nile Delta town of Al-Mahalla Al-Kobra.
"The people want to bring down the regime," they chanted in Cairo's Tahrir Square, echoing the slogan that rang out there less than two years ago and brought down Hosni Mubarak.
Mursi plunged Egypt into a new crisis last week when he gave himself unlimited powers and put his decisions beyond judicial challenge, saying this was a temporary measure to speed Egypt's democratic transition until the new constitution is in place.
His assertion of authority in a decree issued on Nov. 22, a day after he won world praise for brokering a Gaza truce between Israel and the Palestinian Islamist Hamas movement, dismayed his opponents and widened divisions among Egypt's 83 million people.
Two people have been killed and hundreds wounded in protests by disparate opposition forces drawn together and re-energized by a decree they see as a dictatorial power grab.
Mursi has also antagonized many of the judges who must by law supervise the referendum. His decree nullified the ability of the courts, many of them staffed by Mubarak-era appointees, to countermand his measures, even though he has promised to uphold the independence of the judiciary.
Yet Mursi's gambit has placed his liberal, leftist, Christian and other opponents in a bind. If they manage to block the constitution in the referendum, the president would presumably retain the powers he has unilaterally assumed.
Egypt's quest to replace the basic law that underpinned Mubarak's 30 years of army-backed one-man rule would also return to square one, creating more uncertainty in a nation in dire economic straits and seeking a $4.8 billion loan from the IMF.'No place for dictatorship'
Mursi's well-organized Muslim Brotherhood and its ultra-orthodox Salafi allies, however, are convinced they can win the referendum by mobilizing their own supporters and the millions of Egyptians weary of political turmoil and disruption.
"There is no place for dictatorship," the president declared on Thursday while the constituent assembly was still voting on a constitution which Islamists say enshrines Egypt's new freedoms.
Human rights groups have voiced misgivings, especially about articles related to women's rights and freedom of speech.
The text limits the president to two four-year terms, requires him to secure parliamentary approval for his choice of prime minister, and introduces a degree of civilian oversight over the military - though not enough for critics.
The draft constitution also contains vague, Islamist-flavored language that its opponents say could be used to whittle away human rights and stifle criticism.
For example, it forbids blasphemy and "insults to any person", does not explicitly uphold women's rights and demands respect for "religion, traditions and family values"
The draft injects new Islamic references into Egypt's system of government but retains the previous constitution's reference to "the principles of sharia" as the main source of legislation.
The Islamist rallies on Saturday were intended as a show of strength after the previous day's demonstrations by tens of thousands of anti-Mursi protesters in Cairo and elsewhere.
The Muslim Brotherhood and its allies said they would avoid Tahrir square, where opposition protesters are camped out.
A Mursi aide who quit when the leader issued his decree expanding his powers, has joined Egypt's biggest opposition movement, a senior opposition figure said on Friday.
Samir Morkos was Mursi's adviser on the transition to democracy and the only Christian in the Islamist leader's team. At least one other presidential adviser has also resigned.
"We fundamentally reject the referendum and constituent assembly because the assembly does not represent all sections of society," said Sayed el-Erian, 43, a protester in Tahrir and member of a party set up by opposition figure Mohamed ElBaradei.
Several independent newspapers said they would not publish on Tuesday in protest. One of the papers also said three private satellite channels would halt broadcasts on Wednesday.
Egypt cannot hold a new parliamentary election until a new constitution is passed. The country has been without an elected legislature since a court ordered the dissolution of the Islamist-dominated lower house in June.
CAIRO (Reuters) -- Islamists planned rallies across Egypt on Saturday in support of President Mohamed Mursi, who has rushed through a constitution to try to quench opposition fury over his newly expanded powers.