IS has already been driven from all the towns it once held, but Prime Minister Haider al-Abadi has said he will not proclaim victory until the jihadists have been cleared from the western desert bordering Syria.
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Troops and paramilitaries had advanced into the desert from the east and north on Thursday at the start of an offensive aimed at inflicting a final defeat on the jihadists.
On Saturday, troops and tribal militia pushed north from Al-Qaim and Rawa, two Euphrates Valley towns recaptured from IS earlier this month, in a pincer movement against retreating IS fighters, one of the operation's two commanders told AFP.
"It's a matter of linking up with the forces advancing from Nineveh" province in the north, the commander said, asking not to be identified.
"The aim of the operation is to clear the desert right up to the Syrian border and hunt down the terrorists who fled into the desert from the towns that have been liberated."
The Hashed al-Shaabi (Popular Mobilisation) paramilitary force, which has played a key role in the offensive, said 100 villages and hamlets had already been cleared of IS fighters.
"The battle for the desert is very important because it's from there that Daesh fighters coming from Syria can attack our defence lines," said Hashed number two Abu Mahdi al-Mohandis, using an Arabic acronym for IS.
In a video posted by the Hashed, Mohandis said the desert was "the last region where Daesh still has a military presence."
He said operations against it were under away over an area of 27,000 square kilometres (10,400 square miles)
But he warned that their completion would not spell the end of IS.
"We must hunt them down in areas that have been liberated and we must arrest them before they slip back into urban areas," said Mohandis, who is widely regarded as the strongman of the Hashed, which is largely composed of Iran-backed Shiite militias.
"We must remain in a state of alert," he added. "Security will not be fully assured until we have complete control of the border with Syria."
At the peak of its power in 2014, IS ruled some seven million people in a territory as large as Italy, encompassing large parts of Syria and nearly a third of Iraq.
It is now being flushed out of its last desert hideouts in Iraq at the same time as its final pockets of control in Syria face simultaneous operations by Russian-backed government forces and US-backed Kurdish-led fighters.
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