Tens of thousands of protesters have filled Cairo's Tahrir Square to denounce a move by Egypt's ruling generals to seize sweeping powers.
Last weekend, the military dissolved parliament, claiming legislative power.
Egyptians are still awaiting the result of presidential elections, which Muslim Brotherhood candidate Mohammed Mursi says must be declared immediately.
The military has defended its new powers, pledging to deal firmly with threats to stability.
In a TV statement, the Supreme Council for the Armed Forces (Scaf) blamed the country's political "division and confusion" on the early release of unofficial results. It said the premature announcement was "unjustifiable".
It did not name the Muslim Brotherhood's Freedom and Justice Party (FJP), which announced on Tuesday that Mr Mursi, had won with 51.74% of the vote, citing official figures.
His opponent, former Prime Minister Ahmed Shafiq, has also said that he is confident of victory.
But Mr Mursi has now secured the support of several leading liberal figures in Egypt, including activist Wael Ghoneim, who played a key role in the January 2011 revolution against Hosni Mubarak's rule.
'Killing' of democracy
Islamist, secular and youth groups backed a call by the Muslim Brotherhood for protests across Egypt after Friday prayers.
The cleric leading prayers in Tahrir Square said Mohammed Mursi was the clear winner in presidential elections last weekend, the Associated Press reports.
Mr Mursi told a news conference that he would accept the outcome no matter what it was, "but we will not allow anyone to manipulate the results".
He added that if he secured victory, Egypt would have a prime minister "accepted by everyone" and a coalition government.
As Mr Mursi addressed reporters, a number of high profile liberal and independent figures gathered around him and gave their backing to a broad-based government.
Wael Ghoneim said that by supporting the Muslim Brotherhood, they were upholding legitimacy.
He said they would not accept that "democracy be killed because it is not bringing to power those whom we agree with".
Veteran broadcaster and independent broadcaster Hamdi Qandil called for a crisis group to be set up to ensure a peaceful handover of power to a new president.
Results from the run-off election were originally due out during the week but have been delayed. In its statement on Friday, the Scaf called on supporters of both candidates to accept the result.
Thousands of people, mostly Islamists, have demonstrated for three consecutive days against the ruling military council's two decrees.
The first decree ordered parliament to be dissolved. It came after a Supreme Constitutional Court ruling that the law on elections to the lower house was invalid because party members had been allowed to contest seats reserved for independents.
The second decree gave the generals complete control over legislation and military affairs until fresh parliamentary elections are held.
The justice ministry has also granted soldiers the right to arrest civilians for trial in military courts until the ratification of a new constitution.
Mr Mursi condemned the military's decision to dissolve parliament and said there was "no need for a declaration that cripples the powers of the coming president".
Human Rights Watch has said the moves suggest there will not be a "meaningful" handover of power to a civilian administration by 30 June and conditions "ripe" for further human rights abuses have been created.
The BBC's Jon Leyne in Cairo reports that opponents of the Brotherhood are now running a concerted campaign to discredit its claim that Mr Mursi won last weekend's presidential election run-off.
On Thursday evening, Mr Shafiq - a former air force commander who served briefly as former President Hosni Mubarak's last prime minister - made his first public appearance since the election to claim victory for himself.
"I am fully confident that I will be the legitimate winner," he told supporters at a Cairo hotel.
Media sympathetic to Mr Shafiq and the Scaf have begun to demonise the Brotherhood, our correspondent says.
One journalist, Gamal el-Ghetani, said the attempt by the Brotherhood to gain power was like the rise of Adolf Hitler in Germany in the 1930s. The newspaper al-Dustour said the Brotherhood planned a bloodbath if Mr Mursi was not declared the winner.
Members of the HPEC have now suggested a result may now be declared on Sunday. An announcement had been expected on Thursday, but officials said hundreds of complaints had been received from the two candidates.