"Iraqi Security Forces advancing rapidly into former Daesh strongholds of central Fallujah," the official said on Twitter.
The Iraqi Army and Shiite militias, backed by US airstrikes, launched the offensive to retake Fallujah on May 22. The governmental forces have already gained control over most of suburbs of the city.
Fallujah, located some 42 miles west of the Iraqi capital of Baghdad, is one of the largest cities in the Anbar province. The Daesh, outlawed in many countries including Russia, has been in control of the city since 2014.