Demonstrators rejected a call from Egypt's Islamist President Mohamed Mursi for a national dialogue after deadly clashes around his palace, demanding the "downfall of the regime" - the chant that brought down Hosni Mubarak.

Mursi said in a televised speech late on Thursday that plans were on track for a referendum on a new constitution on December 15 despite clashes that killed seven people. He proposed a meeting on Saturday with political leaders, "revolutionary youth" and legal figures to discuss the way forward after that.

But a leading activist group rejected the offer, and fresh demonstrations were called for Friday.

The "April 6" movement, which played a prominent role in igniting the revolt against Mubarak said on its Facebook page that Friday's protests would deliver a "red card" to Mursi.

Egypt has been plunged into turmoil since Mursi issued a decree on November 22 awarding himself wide powers and shielding his decisions from judicial review.