The first protest in December was sparked by the arrest of bodyguards for a Sunni member of Maliki's government, but the issues raised in the Sunni stronghold have become deeper The Washington Post said Friday.
Similar demonstrations have been held elsewhere in the Sunni area of Iraq. They resemble the mass protests that led to the overthrow of authoritarian governments in Tunisia and Egypt and swelled into civil war in Syria.
Thousands of people have been on the streets every Friday in Fallujah. While the demonstrations have been peaceful, leaders warn that might not last.
Hamid Ahmed al Hashem, the head of the local council, said he supports the protesters but appears fearful of what could happen.
"It is very dangerous," he told the Post. "The demonstrators are fed up and we don't know for how long they will be patient. Maybe we won't be able to control them if they get really frustrated."