At least 11 Iraqi soldiers and allied fighters have been killed and 61 others injured in fighting with ISIL in the north of the Iraqi capital, Al Jazeera sources have said.

Fierce fighting took place on Sunday in the Sayed Ghareeb area in Al-Dujail district south of Salah El-din province in Iraq.

One policeman and three others were also killed from Sahwa (Awakening Movement) and five others were injured in ISIL shelling on police positions and barracks in the nearby central Iraqi town of Amiriyat Fallujah, the sources added. 

Salah El-din is just one of the areas which the government is struggling to secure from ISIL attacks.

Missiles were launched from the eastern side of Amiriyat Fallujah, located southeast of the city of Fallujah.

Meanwhile, the Prime Minister Haider al-Abadi on Sunday made a plea to his Australian counterpart Tony Abott to step up military assistance to aid Baghdad's fight against ISIL.

Abbot was on a visit to Iraq to discuss bilateral cooperation between the two countries. Australia is part of a US-led coalition carrying out air strikes against ISIL.

Abadi "called on the Australian side to increase the arming and speed up the training and distribution of what is needed by the Iraqi forces to decide the battle and eliminate the (IS) organisation," his office said.

The IS-led offensive in Iraq began last June, and the group's rapid expansion and brutality in areas it controls in Iraq and neighbouring Syria eventually sparked an international campaign against it.