Abadi has said he will not declare the jihadists have been defeated until they have been cleared from the dry valleys and other natural hideouts that have provided them with a desert refuge since they lost their last urban centres last month.
Troops and paramilitary Hashed al-Shaabi forces "launched a major drive to clear areas of the Al-Jazeera region between Nineveh and Anbar (provinces) in the second phase of operations," Joint Operations Command said in a statement.
JOC spokesman General Yahya Rassoul said on November 27 that they had already cleared 50 percent of the total area of the desert of around 29,000 square kilometres (11,000 sq miles).
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 confined to just a few small pockets, most of them in the desert.