Iraqi forces recaptured a key bridge and several areas near Falluja on Sunday, army sources said.
Iraqi Army and allied militias took control of a bridge at al Sheeha and cut off a supply line controlled by DAESH north of Falluja, a militia spokesman said.
The Iranian-backed Popular Mobilisation Units (PMU) supports the Iraqi Army in its fight against DAESH.
Iraqi forces have suffered a number of defeats against DAESH, but PMU forces played a key role in recapturing the city of Tikrit from DAESH terrorists in March. Tikrit was the home city of Iraq’s former leader Saddam Hussein.
DAESH terrorists deployed two car bombs to break Sunday’s advance from Iraqi forces, killing 21 troops and militia members, army sources said.
The Anbar province stretches from the capital Baghdad to the Syrian border and contains strategic roads that link Iraq to Syria and Jordan.
DAESH terrorists are still fighting in the town of Baiji, home to Iraq's largest oil refinery.
A US-led coalition has been conducting air strikes against DAESH in Iraq and Syria for months.
In Baghdad, four separate bombs exploded on Sunday killing at least 12 people. No group has claimed responsibility for the attacks.