The Iraqi army has stormed the southern edge of Falluja under US air support, and captured a police station inside the city limits.
An elite military unit, the Rapid Response Team, is leading what is shaping up to be the biggest assault ever fought against the so-called Islamic State.
Explosions and gun fire was reportedly seen in Naimiya, a district of Falluja on its southern outskirts.
Separately, Kurdish security forces announced advances against IS in northern Iraq, capturing villages from militants outside Mosul, the biggest city under militant control.
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