Two campaigns to take down "Islamic State" (IS) in Iraq kicked off on Sunday in a double-sided push to retake the terrorists' last two strongholds in the country.

As an Iraqi army offensive around Fallujah completed its buildup, Kurdish peshmerga forces fought to reclaim areas surrounding the city of Mosul.

A force of some 5,500 peshmerga launched an operation east of Mosul early Sunday and had retook the town of Mufti after six hours, a statement for the Kurdistan Region Security Council said.

"This is one of the many shaping operations expected to increase pressure on ISIL (IS) in and around Mosul in preparation for an eventual assault on the city," read the statement.

At the same time, Iraqi special forces were poised to begin their siege of Fallujah, a city 40 miles (65 km) west of Baghdad. Backed by aerial support from the US-led coalition against IS, the army has already recaptured 80 percent of the area surrounding the city in the week since the offense began, according to a military spokesman.

"I won't tell you hours but the breach of Fallujah will happen very soon," said Hadi al-Ameri, a senior commander of a paramilitary force assisting in the operation, to Iraqi television.

Terrorists launch revenge attack

In retaliation for the renewed push-back, IS launched at an attack on the city of Hit in western Iraq on Sunday. The jihadists claimed to have killed 40 government fighters protecting the town.

The cities of Fallujah and Mosul have been under IS control since the terrorists swept through Iraq and Syria in 2014 and captured large pieces of territory. In that time, the jihadists have killed hundreds of civilians and destroyed many of the two towns' ancient ruins amidst a deteriorating humanitarian situation.

es/rc (AFP, AP, dpa)