By Yasmine Saleh

CAIRO (Reuters) - Hundreds of Egyptian liberals and leftists rallied in Cairo on Friday to demand that Islamists stop foisting their ideas upon society, saying the days of one-party rule ended with the overthrow of Hosni Mubarak.

The turnout was less than organizers had hoped, suggesting opponents of Islamist President Mohamed Mursi have yet to capitalize on any popular disapproval with his first three months in office.

Clashes a week ago between Brotherhood supporters and their opponents left more than 100 people injured. Some Brotherhood officials voiced regret over last week's violence and the Islamist movement did not call for a counter-protest this time.

An Islamist-dominated body writing Egypt's new constitution released a draft this month that was met with suspicion by rights groups and liberals seeking to protect personal freedoms.

Mursi hails from the Muslim Brotherhood, a movement that Mubarak tried to suppress and now dominates politics after winning Egypt's first free and fair elections in decades.

He has pledged to defend the cause of Egypt's January 2011 uprising against Mubarak that was driven by anger at a corrupt, autocratic elite.

Opponents say he is repeating history by monopolizing power and is failing to crack down on religious zealots who threaten personal freedoms and Egypt's large Christian minority.

"Down, down Mursi-Mubarak," a few hundred protesters yelled as they marched towards Tahrir Square, cradle of the 2011 uprising. "Hold on, country. Freedom is being born."

At least 20 organizations ranging from human rights groups to revolutionary socialists, opponents of military trials, nationalists and liberals joined the protest.

By mid-afternoon, some 2,000 protesters were shouting their demands in Tahrir Square under banners proclaiming: "The people want a constitution for all Egyptians."

Some opposition parties are trying to unite to avoid another poor showing in a parliamentary election, due to take place once the long-delayed constitution is ratified in a referendum.

(Reporting by Yasmine Saleh; Writing by Tom Pfeiffer; Editing by Michael Roddy)