"The operation aims to liberate Bashir, after we succeeded several days ago in cutting off supplies to (IS) in the Bashir area," said Abu Ridha al-Najjar, who is leading the operation.
Sheikh Maitham al-Zaidi, the commander of Furqat al-Abbas, one of the groups involved, also confirmed that the operation had begun.
Najjar said that nine pro-government fighters were killed and 60 wounded in clashes with IS on Sunday.
The jihadist group fired rockets suspected of carrying a mustard agent last month from Bashir on Taza Khurmatu, another town in the northern province of Kirkuk.
The attack killed three children, wounded a large number of people and pushed thousands more to flee Taza out of fear that it would be repeated.
IS overran large areas north and west of Baghdad in 2014, but has since lost significant ground to Iraqi forces backed by US-led air strikes and training.
IS has used chemical agents in the past, a tactic which has caused few casualties and whose impact so far has been more psychological than military.
When faced with the initial IS offensive in June 2014, Baghdad turned to Shia paramilitary forces dominated by Iran-backed militias to help halt the onslaught and then to push the jihadists back.
These forces, organised under an umbrella organisation called the Hashed al-Shaabi, have been effective in fighting the jihadists, but some members have also carried out extrajudicial killings, kidnappings and destruction of property.
