In Cairo one person was detained and several others injured during clashes between opposition protesters and police.
The rally was organised by two of Egypt’s most active grassroots groups, the Sixth of April Youth and Kefaya which means “Enough”.
Scuffles broke out when some of the demonstrators tried to break through a police cordon.
They are calling for an end to President Hosni Mubarak’s 29-year rule, changes to the Constitution and for emergency law to be repealed which allows for indefinite detention.
The protest follows a police crackdown earlier this month when 93 demonstrators were arrested, but later released.
Egypt is due to hold parliamentary elections later this year and a presidential vote the next.
President Mubarak’s ruling party is expected as usual to dominate the assembly.