The assault, together with another further north, left at least 22 people dead and came as pro-government forces were making major gains on the fifth day of their advance on the last major urban centre held by the Islamic State group in Iraq.
An AFP correspondent saw a group of men carrying rifles and grenades and wearing "Afghan-style clothes" walk down a street in Kirkuk, an ethnically divided city to the south of Mosul under Kurdish control.
At least five suicide bombers struck government targets in the city, including the main police headquarters, in a coordinated attack that began in the middle of the night.
The Islamic State jihadist group claimed the attack, according to the IS-affiliated Amaq news agency.
Gunfire and explosions echoed across the city all morning, residents said, and live footage on local television showed street battles in several neighbourhoods.
"They will increasingly use terror attacks and go back to more of a pure insurgent and terrorist organisation in Iraq."
"Around morning prayers, I saw several Dawaesh (IS fighters) enter Al-Mohammadi mosque," Haidar Abdelhussein, a teacher who lives in the Tesaeen neighbourhood, told AFP.
"They used the loudspeakers to shout 'Allahu Akbar' (God is greatest) and 'Dawla al-Islam baqiya' (Islamic State will remain)," he said.
The governor of Kirkuk, Najmeddin Karim, told AFP he suspected the involvement of IS sleeper cells.
According to Amaq, the jihadist group claimed to control half of the city but reports from witnesses and security officers suggest that may be an exaggeration.
Kirkuk lies 240 kilometres (150 miles) north of Baghdad, in an oil-rich region. The large city is ethnically and religiously divided but currently under Kurdish control.
Insurgent tactics
Kurdish peshmerga fighters have played a major role in the advance on Mosul -- Iraq's biggest military operation in years -- and both they and federal security forces have made gains on several fronts.
Political and military leaders have praised what they say is faster than expected progress, with IS offering deadly but so far ineffective resistance as forces backed by air strikes steamroller towards the edge of Iraq's second city.
The jihadists defending the city where Abu Bakr al-Baghdadi proclaimed a "caliphate" in June 2014 are vastly outnumbered and the final outcome is hardly in doubt.
But they have been launching countless suicide bombers against advancing Iraqi forces to make the anti-IS drive as slow and painful as possible.
Also on Friday morning, gunmen wearing suicide vests stormed a power plant being built by an Iranian company near Dibis, a town southeast of the Mosul offensive's main area of operations, and just 40 kilometres (25 miles) from Kirkuk.
"Three suicide bombers attacked the power plant at around 6:00 am (0300 GMT), killing 12 Iraqi administrators and engineers and four Iranian technicians," Dibis mayor Abdullah Nureddin al-Salehi told AFP.
A police lieutenant colonel confirmed the casualty toll from the attack, which was also claimed by IS.
Huge peshmerga push
A Kirkuk official told AFP that a total curfew was slapped on the city, which had turned into a war zone on Friday.
The jihadist group controlled more than a third of Iraq two years ago but its self-proclaimed "caliphate" has been shrinking steadily since.
A 60-nation US-led coalition and neighbouring Iran have been helping Iraqi forces to regain one city after another and Mosul is now the group's last major stronghold in the country.
The group's days as a land-holding force in Iraq are almost over and it does not appear able to launch major ground counter-offensives as it had done in the past when under attack.
"But they will increasingly use terror attacks and go back to more of a pure insurgent and terrorist organisation in Iraq," said David Witty, an analyst and retired US special forces colonel.
IS claimed responsibility for at least five suicide car bomb attacks against Kurdish forces attacking their positions northeast of Mosul.
"Up to 10,000 peshmerga are involved in this operation from three fronts, making it one of the largest ground-led assaults in the war against ISIL," the peshmerga command said in a statement, using an alternative acronym for IS.
Number of displaced rising
Iraqi forces have not provided figures for their losses but the statement said "a number of peshmerga have paid the ultimate sacrifice."
It also said "global coalition warplane and support were not as decisive as in the past" but did not explain why.
The coalition announced that a US service member accompanying elite Iraqi forces northeast of Mosul was killed on Thursday when an improvised explosive device struck his vehicle.
On Thursday, Iraqi forces retook Bartalla, a mostly Christian town barely 15 kilometres (10 miles) east of Mosul and now one of the spots where anti-IS troops are closest to the city.
The same forces from the elite counter-terrorism service were now expected to move on nearby Qaraqosh, once the largest Christian town in Iraq.
Iraqi forces were also working their way up the Tigris Valley from the south, retaking village after village and meeting limited numbers of fleeing civilians.
According to the United Nations, 5,640 people were displaced in the first three days of the operation Prime Minister Haider al-Abadi declared on October 17.
"The number of vulnerable people moving to areas of safety is expected to rise as hostilities intensify closer to urban areas," it said.
It said up to 1.2 million people may still be inside Mosul, trapped by the estimated 3,000 to 4,500 IS fighters digging in for a major urban assault by the advancing Iraqi forces.
The aid community fears an exodus of massive proportions that could peak as winter sets in without sufficient shelter capacity for the displaced.
