"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 four pro-government fighters were killed and 40 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.
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 Shiite paramilitary forces dominated by Iran-backed militias to help halt the onslaught and then to push the jihadists back.
