The action was concentrating on the town of Husaybah, east of Ramadi.
Shia militias began gathering for a counter-offensive after IS fighters captured Ramadi last Sunday.UN concern over Ramadis displaced by IS advance
The largest concentration is at Bzebiz bridge which has been closed by the authorities to prevent those fleeing from entering Iraq's capital, Baghdad.
IS seized Ramadi earlier this week and Pro-government militias are preparing an offensive to retake the city.
IS militants are reported to be pressing eastwards from Ramadi - capital of Anbar province - down the Euphrates Valley towards Habbaniya where the Shia militias have been deployed.