"We warn al-Maliki that the people of Anbar have another choice, if their demand is not met," Abu Risha told supporters in a televised statement Saturday.
Seven people were killed and 47 others were wounded Friday in Fallujah when soldiers opened fire at an anti-government protest.
Abu Risha also demanded Maliki withdraw troops from Fallujah ahead of Saturday morning's funeral procession for those killed.
"They need to go back to their barracks and be stopped, or there may be losses among their ranks or the ranks of the police. With all honesty, Fallujah is boiling," he said.
Thousands of mourners gathered in Fallujah Saturday for the funeral procession, chanting slogans such as "God is great, God is great" and "al-Maliki is the enemy of God."