Egyptian police have fired tear gas and used water cannons at stone-throwing protesters outside the presidential palace as the opposition held rallies to mark the second anniversary of Hosni Mubarak's overthrow.

The clashes on Monday broke out after several hundred protesters marched to the palace, the site of increasingly frequent clashes, on a day of marches against Egypt's current president, Mohamed Morsi.

Opposition groups called for the protests to demand that Morsi fulfil the goals of the revolution which brought him to power along with his long-banned Islamist  group, Muslim Brotherhood.

Among their key demands are a new unity government, amendments to a controversial constitution and the sacking of Egypt's prosecutor general.

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Activists are also furious that no one has been held accountable for the deaths of dozens of protesters in past months in clashes with police.

"Down with Brotherhood rule," the protesters chanted as they made their way to Cairo's Tahrir Square, the symbolic heart of protests that toppled Mubarak.

Other marches converged on the palace.

Earlier, protesters briefly blocked a major bridge as well as trains in a central Cairo metro station, scuffling with passengers and metro police, witnesses and state media reported.

Two years ago, Egyptians poured onto the streets to celebrate after an aide to Mubarak announced the veteran president's resignation, buoyant that democratic change was within reach.

Mubarak's fall from grace on February 11, 2011, after an 18-day popular revolt sent shock waves across the Middle East and beyond.

But two years later, many are angry the main goals of freedom and social justice have not been achieved and that Egypt is polarised between Morsi's supporters and a broad opposition.

Egypt has witnessed deadly violence, insecurity and price hikes, heightening the political turmoil gripping the country.