( CNN ) -- Tribal leaders in Falluja called Tuesday on people who fled weekend fighting between al Qaeda-linked fighters and government troops to return , a signal efforts were underway to dial back the violence that has raised questions about the ability of Prime Minister Nuri al-Maliki to hold Iraq together . In the statement released to CNN , tribal and religious leaders called on government employees and other workers to return to work Wednesday . `` All residents and families who have fled recent fighting should return as well , '' it said . Even as Sunni tribal leaders issued the call , government troops took up stronger positions within sight of the city , according to a journalist in Falluja working for CNN . Conflicting reports emerged over the weekend about who was in control in Falluja , the site of some of the bloodiest fighting between U.S. forces and insurgents during the Iraq War . Some suggested the Islamic State of Iraq and Syria ( ISIS ) , formerly the group commonly known as al Qaeda in Iraq , is in partial control of the city , which is situated roughly 60 kilometers ( 37 miles ) west of Baghdad , in the volatile province of Anbar . The government said this weekend that the Iraqi army shelled Falluja in an effort to clear out the al Qaeda-linked fighters . The statement came a day after al-Maliki ordered Iraqi forces not to target residential neighborhoods in Falluja . It 's unknown whether a deal between the Sunni tribal leaders and the Shiite-dominated government prompted what appears to be a clear effort to calm the situation . The journalist working for CNN has seen people moving freely in and out of Falluja , though Sunni tribal forces are manning checkpoints . CNN is not identifying the journalist out of concern for his security . Violence has flared in the province following the arrest of a Sunni lawmaker in Ramadi and the dismantling of protest sites by the army in Falluja and Ramadi . CNN 's Saad Abedine and Joe Sterling contributed to this report .
Statement released to CNN calls on government workers to return to work in Falluja . It also calls on residents who fled weekend fighting to return . A journalist in Falluja says people are moving freely through checkpoints .