The Iraqi government and a powerful group of Shia fighters have declared victory over the the Islamic State of Iraq and the Levant group in the key Iraqi province of Diyala.

The offensive was led by the Badr Brigade, a Shia group backing the Iraqi army.

The group held a victory rally on Monday and said it was ready to move north into ISIL strongholds.

Al Jazeera's Jane Arraf, reporting from Baghdad, said that Shia militias, in particular the Badr Brigade, have overshadowed government forces in the conflict.

She noted that Hadi al-Amri, the brigade's leader and a former tansport minister, said his group is working with tribes to take back the provinces of Anbar and Mosul from ISIL.

Shia fighters and government forces have also been accused of committing war crimes in Diyala province, Arraf said.

"Around the capital of Diyala province, there is a town called Barwana, where surivors tell us that Shia militia forces along with Iraqi government forces killed unarmed civilians," our correspondent said.

She said the survivors had spoken to Al Jazeera by telephone over the past several days.

Arraf said al-Amri, in a brief interview at Camp Ashraf in Diyala following the victory celebration, said any claims were being investigated and any culprits would be brought to justice.

The central government forces, various tribes and Kurdish fighters controlled by the Kurdish government in northern Iraq have been battling the ISIL, which has also come under sustained air strikes by a US-led coalition.

ISIL captured large swaths of territory in Iraq and Syria in an offensive last year, plunging Iraq into its worst crisis since US troops left at the end of 2011.

Defeat of ISIL in Diyala comes only days after another major blow to the armed group in neighbouring Syria. On January 26, Kurdish fighters in northern Syria took control of the fiercely-contested Syrian city of Kobane from ISIL forces after more than three months of fighting.