Clashes were earlier reported in Qom after Ayatollah Montazeri's funeral
Iranian security forces and opposition activists have clashed in Tehran, reformist websites and witnesses say.
Some reports say shots have been fired in the air to disperse demonstrators in the centre of the capital.
Clashes were also reported in northern Tehran, where reformist ex-President Mohammad Khatami had been due to speak.
The opposition had sought to use Shia religious festivals this weekend to show its defiance of President Mahmoud Ahmadinejad's government.
Tensions have risen since influential dissident cleric Grand Ayatollah Hoseyn Ali Montazeri died a week ago aged 87.
Clashes were reported after his funeral in Qom, and in other cities since then.
Police chief Esmail Ahmadi Moghaddam has been quoted as warning that police would crack down hard against any attempts to use Shia religious processions to stage fresh protests against Mahmoud Ahmadinejad's government.
Opponents insist there was massive rigging when Mr Ahmadinejad was re-elected in June - a charge he rejects.
BBC Tehran correspondent Jon Leyne says opposition sources are building a picture of increasingly widespread and violent clashes.
Saeed Barzin, Iran analyst - BBC Monitoring
This was expected to happen - opposition websites have been agitating, calling on people to come onto the streets for these particular days, although the opposition leaders have not issued statements calling on people to do so.
Nevertheless we are seeing people taking risks to join the demonstrations.
The police are trying to take the initiative early in the day, prevent the crowds from building up and keeping crowds in neighbourhoods, localising the situation; the police commander has said they will be firm but they will try to use minimal force against protesters.
Unconfirmed reports on reformist websites said there were protests in several areas of the capital, including the poorer areas of south Tehran, and that government forces were using tear gas to try to disperse demonstrators.
A witness quoted by Reuters news agency said opposition supporters had gathered in groups along a stretch of a main city centre route several kilometres long, but that police were not letting them join each other.
AFP news agency said police had "sought to disperse about 200-300 people" planning to demonstrate in central Enghelab square as part of a Shia festival.
Government forces are said to reacting aggressively - beating protesters with batons and smashing the windscreens of cars.
Later on Saturday, demonstrators clashed with riot police near a mosque in northern Tehran where Mr Khatami had been due to speak, witnesses and opposition websites say.
They say riot police also fired tear gas during the incident.
Shia religious festivals on 26-27 December mark the death of a grandson of the Prophet Muhammad in the 7th Century.
The main date set by reformists for demonstrations is Sunday.