Recapturing Fallujah, the first city to fall to the Islamic State group more than two years ago, means that authorities can now set their sights on militant-held Mosul, Iraq's second-largest city.

Prime Minister Haider al-Abadi, visiting central Fallujah with the celebrating troops, vowed that the Iraqi flag would next be raised above Mosul. But that campaign has been progressing in fits and starts, revealing the deep divisions among the different groups that make up the security forces.

Iraqi troops entered Fallujah's northwestern neighborhood of al-Julan, the last part of the city under IS control, said Lt. Gen. Abdul-Wahab al-Saadi, head of the counterterrorism forces in the operation.

The operation, which began May 22, "is done, and the city is fully liberated," al-Saadi told The Associated Press.