KIRKUK, Iraq — Iraqi state television said early Monday that Iraqi forces had begun an operation to seize the Kurdish-held city of Kirkuk and its surrounding oil fields, despite weeks of urgent efforts by the United States to keep tensions between its allies from boiling over into another war in the Middle East.

In a brief statement released to the state-run network, Iraq’s prime minister, Haider al-Abadi, ordered troops to impose security in the area “in cooperation with the people of Kirkuk and the pesh merga,” or Kurdish fighters.

State-run TV said the initial assault by Iraqi troops, counterterrorism forces and federal police did not encounter resistance as they sought to reclaim areas seized by Kurdish forces in 2014. But there were unconfirmed reports of clashes with the pesh merga, who maintain defensive lines around Kirkuk and the oil fields.

Military sources also reported exchanges of artillery fire, but those reports could not be confirmed.