(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.