The Iraqi army has gained control of Fallujah's southern al Shuhada II district as an offensive against Daesh stronghold west of Baghdad continues for a third week, the military said.

Elite anti-terrorism forces were advancing deeper into the city, 50 kilometres west of the capital Baghdad, an army statement said.

Prime Minister Haider al-Abadi's official Facebook page posted what it said were pictures of the premier touring the district, with Daesh graffiti visible on a wall behind him in one photograph.

Al-Abadi announced the offensive against Fallujah, a stronghold of the Sunni extremist group since early 2014, on May 23.

Government forces backed by Shia militias and US-led airstrikes have captured wide areas surrounding the city from the militants since then.

But the counterterrorism forces, the best-trained in the Iraqi army, have met stiff resistance inside the city, where they say the militants have dug a network of tunnels allowing them to launch surprise attacks on advancing troops.

The offensive has been marred by allegations that the Shia militias used to clear outlying areas have mistreated locals fleeing the mainly Sunni city, with anger growing over widely circulated videos apparently showing civilians being beaten or treated after torture.

Al-Abadi on Tuesday said that those responsible for abuses had been arrested and referred to the courts, but also warned against exaggerated claims.

Daesh has lost considerable ground in western Iraq in recent months, but still controls Iraq's second city, Mosul, in the north; Albawaba reported.

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