The demonstrations on Sunday, called by Sunni leaders, also called for the release of detainees and the payment of long-promised compensation for the destruction caused by a US offensives which were backed by the Iraqi government.
There were also calls for the cancellation of the recent government decision to triple the price of petrol, which has provoked angry demonstrations throughout the country.
In a petition, demonstrators in Falluja demanded "new elections" on the grounds that the results of the 15 December poll had been falsified - a charge also levelled by Sunni Arab leaders and the list of Iyad Allawi, the former prime minister who is a secular Shia. His coalition includes some Sunnis and communists.
Massive demonstrations organised by the National Concord Front, the main Sunni electoral alliance of three parties, took place in Baghdad on Friday as well in a number of cities north of the capital.
In Baquba on Sunday, demonstrators representing the alliance held banners saying: "We will not allow Iraq to be divided".
Shia groups in the Baghdad neighbourhood of Sadr City, on the other hand, demonstrated on Saturday for the Shia coalition of Ibrahim al-Jaafari, the current prime minister, to maintain his job in the new government.