Iraqi government forces have captured key installations outside the disputed city of Kirkuk from Kurdish fighters.
A military statement said units had taken control of the K1 military base, the Baba Gurgur oil and gas field, and a state-owned oil company's offices.
Baghdad said the Peshmerga had withdrawn "without fighting", but clashes were reported south of Kirkuk.
The operation was launched a month after the Kurdistan Region held a controversial independence referendum.
Iraq's prime minister has said the vote - in which residents of Kurdish-controlled areas, including Kirkuk, overwhelmingly backed secession - was unconstitutional.
The Kurdistan Regional Government (KRG) insisted it was legitimate.
US officials said they were "engaged with all parties in Iraq to de-escalate tension".
What does the government want?
Prime Minister Haider al-Abadi said in a statement that the operation in Kirkuk was necessary to "protect the unity of the country, which was in danger of partition" because of the referendum.
"We call upon all citizens to co-operate with our heroic armed forces, which are committed to our strict directives to protect civilians in the first place, and to impose security and order, and to protect state installations and institutions," he added.
Earlier, the Iraqi military announced that elite units had been "re-deployed" at the K1 base, about 5km (3 miles) north-west of the city of Kirkuk, and that other troops had taken control of the nearby Leylan area, the Baba Gurgur oilfield, and the headquarters of the North Oil Company.
The military also said troops had taken control of a military airport, police station, power plant and several industrial areas, as well as key bridges, roads, junctions.
The Kurdistan Region Security Council accused Baghdad of launching an "unprovoked attack" and said the Peshmerga would "continue to defend Kurdistan, its peoples and interests".
Peshmerga had destroyed five US-made Humvees used by the Popular Mobilisation, a paramilitary force dominated by Iran-backed Shia militias, it added.
Peshmerga spokesman Brig Gen Bahzad Ahmed told the Associated Press that the fighting south of Kirkuk had caused "lots of casualties". He alleged that pro-government forces had also "burnt lots of houses and killed many people" in Tuz Khurmatu, 75km south of Kirkuk, and Daquq.
There was no way of verifying the reports, but a doctor at a hospital in Tuz Khurmatu told AFP news agency that two people had been killed by artillery fire.
The US-led coalition against IS, which supports both Iraqi government and Peshmerga forces, said it had so far only seen "co-ordinated movements" by military vehicles around Kirkuk and "not attacks".
A limited exchange of fire before dawn was the result of a "misunderstanding and not deliberate as two elements attempted to link up under limited visibility conditions", a statement added.
What's happening inside Kirkuk?
By Orla Guerin, BBC News
On the streets of Kirkuk we have seen armed Kurdish civilians - old and young, but almost no Kurdish security forces. One man told us he was ashamed the Peshmerga had abandoned some positions outside the city overnight.
We have heard plenty of defiance from locals. "If we have to die, we will die here in our city," one man said.
But the city has been shutting up shop in the past few hours, with the roads emptying and people rushing for home.
As we filmed at the main checkpoint at the southern edge of Kirkuk there was a sudden burst of automatic gunfire. It seemed to come from a location where Shia militia units are in position.
Why is Kirkuk disputed?
Kirkuk is an oil-rich province claimed by both the Kurds and the central government. It is thought to have a Kurdish majority, but its provincial capital has large Arab and Turkmen populations.
Kurdish Peshmerga forces took control of much of the province in 2014, when Islamic State (IS) militants swept across northern Iraq and the Iraq army collapsed.
The Iraqi parliament asked Mr Abadi to deploy troops to Kirkuk and other disputed areas after the referendum result was announced, but he said last week that he would accept them being governed by a "joint administration" and that he did not want an armed confrontation.
On Sunday, his cabinet accused the KRG of deploying non-Peshmerga fighters in Kirkuk, including members of the Turkish Kurdistan Workers' Party (PKK), which it said was tantamount to a "declaration of war". But KRG officials denied this.
Why does this matter?
By Jonathan Marcus, BBC diplomatic correspondent
These are the opening moves in what threatens to be a new conflict in Iraq; a battle for the control of territory captured from IS.
Kurdish fighters are emboldened by the recent referendum which saw a huge vote for Kurdish independence.
The Baghdad government will take the view that it is simply seeking to restore the status quo prior to the emergence of IS.
To say things are complicated is an understatement.
The Kurds themselves are divided. Other ethnic militias have their own interests to defend.
And the US seems unable to halt the fighting as it watches US trained and armed Iraqi units confront Kurdish groups who are also Washington's allies.