Iraqi forces battled Sunday through booby-traps, sniper fire and suicide car bombs to tighten the noose around Mosul, while also hunting Islamic State group jihadists behind attacks elsewhere in the country.

Kurdish forces announced a new push at dawn Sunday on Bashiqa northeast of Mosul where some 10,000 fighters are engaged in a huge assault to take the IS-held town.

The push came with US Secretary of Defense Ashton Carter in Iraq’s autonomous region of Kurdistan to support the unprecedented offensive, which a US-led coalition is backing with air and ground support.

Launched last Monday, the assault aims to reclaim the last major Iraqi city under IS control, dealing another setback to the jihadists’ self-declared "caliphate" in Iraq and neighboring Syria.

The jihadists hit back on Friday with a surprise assault on the Kurdish-controlled city of Kirkuk and two days later security forces were still tracking down fighters involved in the attack.

The dozens of attackers, including several suicide bombers, failed to seize control of key government buildings but sowed chaos in Kirkuk, a large oil-rich and ethnically mixed city.

At least 51 of the jihadists had been killed, including three more on Sunday, local security officials said.

Sporadic clashes continued, a senior security official said, with forces besieging IS gunmen in Kirkuk’s Nidaa neighborhood.

At least 46 people, most of them members of the security forces, were killed in the raid and ensuing clashes.

Kurdish and other forces were also tracking down jihadists believed to have fled Kirkuk on Saturday to rural areas east of the city.

IS jihadists also attacked Rutba, a remote town near the Jordanian border in the western province of Anbar, with five suicide car bombs, the area’s top army commander said on Sunday.

The attackers briefly seized the mayor’s office but security forces quickly regained the upper hand, he said.

- Fierce IS resistance -

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The spectacular attack in Kirkuk, of a type observers warned could happen more often as IS loses territory and reverts to a traditional insurgency, temporarily drew attention away from Mosul.

But there was no sign it had any significant impact on the offensive to retake the city, Iraq’s largest military operation in years.

On a trip to Iraq to review the operation, Carter met Prime Minister Haider al-Abadi on Saturday and Kurdish leader Massud Barzani on Sunday.

The United States leads a 60-nation coalition -- which also includes Britain and France -- that has provided support in the form of thousands of air strikes, training for Iraqi forces and advisers on the ground.

Tens of thousands of fighters, including Iraqi federal troops and Kurdish peshmerga, are taking part in the assault.

Engaged on the northern and eastern fronts, the peshmerga are expected to stop along a line at an average of 20 kilometers from the boundaries of the city proper.

"They are pretty much there," a US military official said on Saturday, adding that the lines "will be solidified in the next day or two."

Elite federal forces are also fighting to retake control of Qaraqosh, which lies just east of Mosul and used to be the largest Christian town in Iraq.

IS fighters swept across the Nineveh plain in August 2014, forcing hundreds of thousands of people to flee, including many Christians and other minorities.

Lieutenant General Stephen Townsend, commander of the US-led coalition, said Saturday that jihadist resistance was stiff.

"It’s pretty significant, we are talking about enemy indirect fire, multiple IEDs (improvised explosive devices), multiple VBIED (vehicle-borne IEDs) each day, even some anti-tank guided missiles," he said in Baghdad.

US military officials have revised their estimate slightly upward for the number of IS fighters in and around Mosul.

- 5,000 displaced -

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They believe IS is defending Mosul, where the "caliphate" was proclaimed in June 2014, with 3,000 to 5,000 fighters inside the city and 1,000 to 2,000 in the outskirts.

A French government official told AFP the breach into Mosul, which could mark the beginning of a phase of fierce street battles with IS, could still be a month away.

There is deep concern for an estimated 1.2 million civilians still believed to be in the city.

Several thousand civilians fleeing the fighting and the jihadists who ruled them for two years have escaped to camps for the displaced south of Mosul.

"Over 5,000 people are currently displaced and in need of humanitarian assistance," the United Nations said in an update on Sunday.

"Population movements are fluctuating as the front lines move, including people returning to their homes following improved security conditions in the immediate area," the statement said.

Iraqi forces are now fighting in sparsely populated areas but when they near the limits of the city itself aid groups fear the start of a huge exodus.

A million people could be displaced, sparking an unprecedented humanitarian emergency in a country where more than three million people have already been forced from their homes since the start of 2014. (AFP)