|Protesters accuse President Morsi of imposing a new form of authoritarianism|
Opposition groups accuse current Islamist President Mohammed Morsi of betraying the goals of revolution.
Mr Morsi's supporters say the protesters want to bring down Egypt's first democratically elected leader.
Hosni Mubarak - who had ruled the country's for almost 30 years - was swept from power in a wave of mass protests on 11 February 2011.
Continue reading the main story'Leave!'
Mostafa Ismael Egyptian bus driverSince Mubarak stepping down, we haven't seen any stability. Thugs are everywhere. All we want is to live in peace and resume our work safely”
Monday's clashes outside the presidential palace reportedly began after some of the demonstrators tried to break through a barbed wire barrier protecting the building's main gate.Some in the crowd chanted: "The people want to bring down the regime!"
The protesters also sprayed graffiti on the palace walls, which read: "Leave!"
There were no immediate reports of any injuries.
Egypt's secular opposition accuses President Morsi - a member of the Islamist Muslim Brotherhood - of imposing a new form of authoritarianism and betraying the values of the 2011 uprising.
Mr Morsi rejects the protesters' claim. Earlier this month, he warned that security forces would "act with utmost decisiveness" to protect state institutions and those groups behind the violence would be held "politically accountable".
The current unrest began on 24 January in Cairo - on the eve of the second anniversary of the revolution.
Protests have since spread to several cities across the country, leaving dozens of people dead and hundreds injured.