A combat unit is advancing in Fallujah as blasts and gunfire are being heard in the city’s southern Naimiya district, an army officer told Reuters.
"Iraqi forces entered Fallujah under air cover from the international coalition, the Iraqi air force and army aviation and supported by artillery and tanks," AFP quoted Lieutenant General Abdelwahab al-Saadi, the commander in charge of the operation, as saying.
Daesh is trying to repel the offensive.
The Iraqi Army backed by militias began the operation on May 23 by encircling the city located some 50 kilometers away from Baghdad, the Iraqi capital, in the Anbar province, and started tightening the siege since then.
In January 2014, Fallujah became the first Iraqi city which fell to Daesh terrorists who captured large swathes of land in the country and neighboring Syria, and later declared a caliphate there. Daesh still controls Mosul, Iraq's second largest city.
On May 22, Baghdad deployed at least 20,000 troops to combat extremists in the city, and told residents to flee Fallujah ahead of the operation. In Iraqi Defense Ministry source said the operation to liberate the city would take "a few days."