Tensions are high in the region after Kurds voted in favor of independence in a referendum.
The non-binding vote was held on September 25 in defiance of warnings from Baghdad, which had vowed to take all "necessary measures" to protect the country's unity.
Baghdad continues to reject decades-old Kurdish ambitions to incorporate Kirkuk and other historically Kurdish-majority areas into their autonomous region.
Iraqi forces and Shi'ite Muslim paramilitaries, known as Popular Mobilisation, are deployed south and west of Kirkuk, after having recaptured the areas from Islamic State (IS).
One of them, Khasro Abdallah, vowed "to defend Kirkuk to the death".
"We will not allow anyone to attack (Kirkuk)", Arass Faqih, another civilian holding a Kalashnikov assault rifle, told AFP.
The Kirkuk province is not officially included in Iraqi Kurdistan, but it is in fact partially controlled by Kurdish Peshmerga detachments.
The Iraqi army and the Kurdish peshmerga have been allies in the US-led coalition against the "Islamic State" (IS) terrorist group. At the time, peshmerga fighters were among the only groups to stand their ground against and eventually repel the IS militants.
Meanwhile, a Justice Ministry official from northern Iraq's autonomous Kurdistan Regional Government (KRG), denounced the Iraqi court's warrants as "politically motivated", stressing that Baghdad's judicial system has no jurisdiction in Kurdistan, which is allegedly ruled by its own legal body. The army officer spoke on condition of anonymity in line with regulations.
"There are threats by the Iraqi Army that has deployed forces near Kirkuk supposedly to attack Kirkuk".
The peshmerga's Kirkuk commander, Sheikh Jaafar Mustafa, said his forces had withdrawn from areas they had entered during their fight against IS in the west of the province last week.
Southern Kirkuk is a strategic prize for both the Kurds and the federal government as it holds coveted oil fields.
The Kirkuk province along with parts of the provinces of Nineveh, Saladin (northern Iraq) and Diyala (eastern Iraq) are disputed between Baghdad and the KRG and inhabited by a mixture of ethnic Kurds, Arabs, and Turkmen.