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Baghdad said the Peshmerga had withdrawn "without fighting", but clashes were reported south of Kirkuk.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.
Iraqi Prime Minister Haider al-Abadi has said the vote, in which residents overwhelmingly backed secession, was illegal and demanded it be annulled.
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?
The Arab-led central government said it had launched the operation in Kirkuk province to "secure bases and government facilities", and also to "preserve the lives and interests" of Kirkuk's Arabs, Kurds, Turkmen and Christians.
On Monday morning, 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 oil field, 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.
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.
REUTERS
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.
- Sykes-Picot: The map that spawned a century of resentment
- Why don't Kurds have a state?
- Iraqi Kurdistan profile
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.
AFP
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. 
Hello, my name is Jack Sparrow. I'm a 50 year old self-employed Pirate from the Caribbean.