Protests have been called for Friday in response to clashes at the 'Accountability Friday' demonstration.
The Constitution Party and the Popular Egyptian Current called for protests to condemn Friday's violence which they blamed on President Mohamed Morsi and the Muslim Brotherhood.
The groups have also demanded an investigation into the violence which left hundreds injured.
Friday's protests, which turned into violent clashes, were initially called for by leftists and liberals to protest against what they described as Morsi’s failure to deliver on his promises during his first 100 days in office.
The Muslim Brotherhood issued an 11th hour call for their supporters to go to the square on the same day, ostensibly to protest the acquittal of defendants in the Battle of the Camel trial. The group also called for demonstrations in support of Morsi's decision to replace the prosecutor general following the verdict.
One of the groups' other demands is the reopening of investigations into the killing and wounding of protesters during and after the revolution, including the events of Friday, 12 October.
"The president is responsible for gathering all information concerning these events from the relevant authorities, and for pushing for rapid trials," said the joint statement issued by the groups.
The statement further called for the implementation of minimum and maximum wages to promote social justice, in addition to reversing a recent decision forcing shops to close early from November.
"The masses went to the streets on Friday dreaming of a constitution for all Egyptians, but some affiliated with the new ruling party (Freedom and Justice Party) denied opposition forces their right to peacefully express their opinion and criticise the ruling party," the statement said.
The Freedom and Justice Party had committed the same mistakes as Mubarak's National Democratic Party, the statement added.