The spokesman for the Joint Operations Command, Brig Gen Yahya Rasool, said in a televised statement that the operation started at dawn today and that government forces are backed by Shiite and Sunni pro-government fighters.
Rasool didn't clarify whether the US-led international coalition is taking part.
This is not the first time the Iraqi government has announced an operation to retake Anbar -- where several key towns, including the provincial capital Ramadi, remain under IS control.
The Islamic State group, also known by the Arabic acronym Daesh, seized large parts of Anbar in early 2014 and captured Ramadi in May.
Iraqi forces, which had been making steady progress against the extremists in recent months with the help of the air campaign, scored a major victory in recapturing Saddam Hussein's hometown of Tikrit last month.
In a brief statement, Iraq's Prime Minister, Haider al-Abadi, vowed to "take revenge from Daesh criminals on the battlefield... And their cowardly crimes against unarmed civilians will only increase our determination to chase them and to expel them from the land of Iraq."
Rasool didn't provide any further details on the ongoing operations. By noon, the country's state TV reported government forces recapturing villages and areas around Fallujah.
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