Fighting began in the western province's desert terrain as Prime Minister Haidar al-Abadi was touring Anbar, visiting Iraqi army units and pro-government Sunnis, his office said.
Army officers said ISIS militants were driven back Wednesday in the Sijariya area east of the Anbar capital Ramadi and Falluja - the region's two key cities, where the ultra-radical Sunni group has been dominant.
ISIS was retreating from Sijariya, trading mortar fire with government forces, military sources said.
A senior Iraqi officer in Ramadi said the purpose of clearing Sijariya was to secure supply routes to the nearby Habbaniya air base and to weaken the terrorists grip on territory connecting Ramadi and Falluja.
Large parts of Anbar had slipped from the government's grasp even before ISIS overran the northern city of Mosul last June and surged through Sunni areas of Iraq.
Security forces and Shiite Muslim paramilitaries have since regained some ground, although core Sunni territories remain under ISIS control.
Iraqi officials have argued for some time that Anbar should be the next major battleground, or that operations should be carried out there in parallel with the northern province of Nineveh, of which Mosul is capital, in order to isolate ISIS in its strategic bastions along the Syrian border.
"In Anbar there are spots under government control and the troops are fighting ISIS," Deputy National Security Adviser Safaa al-Sheikh told Reuters in late March, using an alternative name for ISIS. "You have these spots and can expand from them. We don't have this situation in Mosul."
Sunni tribes played a key role in driving out al-Qaida in Iraq - a precursor to the Islamic State group - and are widely seen as the only force capable of securing the country's northwest Sunni heartland.