Funerals for several of the seven people killed in Wednesday night clashes between Morsi supporters and opponents -- all said to be members of the Muslim Brotherhood which backed him for the presidency -- were to be held on Friday, the traditional day of Muslim prayer and rest.
Opposition coalition the National Salvation Front called for more mass demonstrations after the main midday prayers, in a possible test for soldiers and anti-riot police guarding the presidential palace with tanks and barbed wire barricades.
The opposition bloc accused Morsi of rejecting "repeated demands to him to offer consensus solutions... to lift Egypt out of its current disastrous situation."
It accused the president of "dividing Egyptians between his 'supporters of legitimacy'... and his opponents, whom he calls 'thugs'."
In a televised speech late on Thursday, Morsi defended giving himself sweeping new powers by decree last month, and said he would push on with a December 15 referendum to change Egypt's constitution along lines drafted by a mostly Islamist panel.
Morsi said he was ready to hold talks with the opposition on Saturday, but showed little inclination to compromise.
The scene outside the presidential palace was calm ahead of noon prayers but security was tight, an AFP correspondent reported.
Around a dozen tanks and armoured troops carriers were deployed in the vicinity, with soldiers and riot police massed behind barbed wire barricades. On Thursday, they had cleared the area.
Protests were expected to swell after the main prayers.
Youth activist group on April 6 called for marches from all of Cairo's mosques to converge on the capital's main squares.
The demonstrations seen this week were the biggest since Morsi took office in June. The street clashes were also reminiscent of the upheaval in February 2011 that toppled veteran strongman Hosni Mubarak.
In his speech late on Thursday, Morsi said the referendum on the constitution would go ahead as planned, adding that "afterwards... everyone must follow its will."
He said: "We respect peaceful freedom of speech but I will never allow anyone to resort to killing and sabotage."
Hundreds of opposition protesters tried to storm the Cairo headquarters of the Muslim Brotherhood as he made his speech, but were pushed back by riot police firing tear gas.
At least four of Morsi's advisers have quit over the crisis, and the Cairo stock market has taken a heavy hit.
The United States and European Union have called for dialogue to resolve the crisis.
US President Barack Obama expressed "deep concern" in a call to Morsi on Thursday, the White House said.
Obama also told Morsi that it was "essential for Egyptian leaders across the political spectrum to put aside their differences and come together to agree on a path that will move Egypt forward."