Thousands of ecstatic supporters of Egyptian President Mohamed Morsi gathered outside the presidential palace on Friday to defend their leader against accusations from rival protesters that he has become a dictator.

"We love you Morsi" chanted his supporters as protesters in Tahrir slammed "Morsi the dicator", highlighting how polarised post-Mubarak Egypt has become.

"Morsi took the decisions we wanted, he is not a dictator at all," said jewellery store owner Mostafa Ammar, 37, dressed in a white robe above the ankle, in prophetic tradition.

"Morsi is on the right track and aims to achieve the goals of the revolution," that toppled Hosni Mubarak last year, said Abu Bakr Abdelkader, 34.

The president's decisions "are definitely revolutionary and come from his revolutionary legitimacy," said teacher Mostafa Shehata, 29.

"The problem is that many don't like to have a Muslim Brotherhood president," he said.

Some waved Egyptian flags, others held up the the green flags of the Muslim Brotherhood, on whose ticket Morsi won the elections in June.

The Islamist president assumed his sweeping new powers in a decree read out by his spokesman Yasser Ali on state television on Thursday.

"The president can issue any decision or measure to protect the revolution," it said.

"The constitutional declarations, decisions and laws issued by the president are final and not subject to appeal."

Morsi also sacked prosecutor general Abdel Meguid Mahmud, whom he failed to oust last month, amid strong misgivings among the president's supporters about the failure to secure convictions of more members of the old regime.

"The president sacked the corrupt general prosecutor who mixed politics and law, so why are others angry?" asked Mohammed Shaaban, a 25-year-old medical student.

On the other side of Cairo, thousands packed Tahrir Square, furious that whatever gains had been made after the revolution that toppled Mubarak have been snatched away in one move his successor.

"It is simply not possible that the revolution happened two years ago, and we moved forward and moved forward, only to have a new dictatorship again," said Nagla Samir.

"We took to the streets for freedom," she said.

Morsi's opponents were led by leading dissidents former IAEA chief Mohamed ElBaradei and Amr Mussa, a former foreign minister and Arab League chief.

With the new decisions, "Mohamed Morsi is saying 'I'm God and my decisions are above everything else'," said Ahmed al-Awady in Tahrir.

On the outskirts of the Tahrir, clashes continued into a fifth day between police and protesters demanding justice for those killed during the 2011 uprising.