Egyptian President Mohammed Mursi has addressed supporters in Cairo in defence of a new decree which gives him sweeping powers and states his decisions cannot be revoked by any authority.

Mr Mursi said he was leading Egypt on a path to "freedom and democracy" and was the guardian of stability.

Protests are being held across the country against the decree and offices of the president's Muslim Brotherhood party have reportedly been attacked in a number of cities.

Police fired tear gas near Cairo's Tahrir Square, heart of the 2011 uprising that toppled Hosni Mubarak, where thousands demanded Mursi Mr quit and accused him of launching a "coup". There were violent protests in Alexandria, Port Said and Suez.

Opponents accused Mr Mursi, who has issued a decree that puts his decisions above legal challenge until a new parliament is elected, of being the new Mubarak and hijacking the revolution.

Aides to Mr Mursi said the presidential decree was intended to speed up a protracted transition that has been hindered by legal obstacles.

"I am for all Egyptians. I will not be biased against any son of Egypt," Mr Mursi said on a stage outside the presidential palace, adding that he was working for social and economic stability and the rotation of power.

"Opposition in Egypt does not worry me, but it has to be real and strong," he said, seeking to placate his critics and telling Egyptians that he was committed to the revolution. "Go forward, always forward ... to a new Egypt."

The United Nations Human Rights Commissioner, Navi Pillay, said the decree raises serious human rights concerns.

The US also expressed concerns about Mr Mursi's decision to assume sweeping powers, the US State Department said.