Iraqi Kurds want to incorporate Kirkuk province into their autonomous region, a move Baghdad strongly has strongly opposed in a bitter, long-running dispute with them.
"We tightened our control of Kirkuk city and are awaiting orders to move toward the areas that are controlled by ISIL," Brigadier General Shirko Rauf of the Kurdish peshmerga security forces told AFP.
He was referring to jihadist Islamic State of Iraq and the Levant, which has spearheaded a major offensive this week that has overrun all of one province and parts of Kirkuk and two other provinces.
Mustafa survived, but the roadside bomb killed a peshmerga fighter.
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Another bomb targeted a peshmerga officer in the Dibs area of Kirkuk province, wounding him and killing his son, who was one of his guards, Rauf added.
Kirkuk Governor Najm al-Din Karim said peshmerga forces had filled gaps left by Iraqi soldiers who withdrew from their positions in the province.
"Army forces are no longer present, as happened in Mosul and Salaheddin," Karim said.
"Peshmerga forces are in control of the majority of the Kurdistan region outside of (Kurdistan Regional Government) administration," Yawar said, referring to the disputed areas.