Iraqi government forces say they have taken control of more disputed areas previously held by Kurdish forces.
The positions in Nineveh province, including the Mosul Dam, had been captured by Kurdish Peshmerga fighters over the past three years during fighting with so-called Islamic State.
Earlier this week, soldiers, police and special forces took control of the city of Kirkuk and nearby oilfields.
The operation came weeks after the Kurds held an independence referendum.
Voters in the autonomous Kurdistan Region and disputed areas then controlled by the Peshmerga overwhelmingly backed secession, but the vote was declared illegal by the Arab-led central government in Baghdad.
Iraqi Prime Minister Haider al-Abadi subsequently ordered troops to take control of all areas claimed by both his government and the Kurdish authorities.
On Tuesday, Kurdish Regional President Massoud Barzani called for peace and vowed to keep working towards Kurdish independence.
He also blamed the loss of Kirkuk on internal disputes between Kurdish politicians.
A sudden switch
By Orla Guerin, BBC News, Kirkuk
A large statute of a Peshmerga fighter still looms over the entrance to Kirkuk, but otherwise there’s little sign left of Kurdish control.
Iraqi forces are now firmly in command, manning new checkpoints on the road to the city.
The city was peaceful but Kurdish areas looked like a ghost town, with shops and homes sealed shut. The thousands who fled the Iraqi advance have not rushed back.
The few people we found on the streets spoke of uncertainty, and loss.
Some were angry at Peshmerga fighters for not defending the city. Others blamed Massoud Barzani for triggering the Iraqi takeover with last month’s independence vote.
A large poster of the president has been damaged by fire. Locals told us Shia militia, officially controlled by Baghdad, set it alight when they entered the city. The burnt portrait is a potent symbol of his loss of authority here.
Why is Kirkuk at the heart of this crisis?
Kirkuk is an oil-rich province and its oilfields are vital to the Kurdish economy. It lies outside the official Kurdistan region and is claimed by both the Kurds and the central government. It is thought to have a Kurdish majority, but its provincial capital also has large Arab and Turkmen populations.
Kurdish Peshmerga forces took control of much of the province in 2014, when Islamic State (IS) group militants swept across northern Iraq and the Iraqi army collapsed.
On Tuesday, Iraqi forces captured the Bai Hassan and Avana oilfields run by state-owned North Oil Company, north of Kirkuk.
A day earlier, troops had captured other key military bases and other oilfields, as well as the governor’s office. Forces pulled down the Kurdish flag, which had been flying alongside the Iraqi national flag, reports said.
Peshmerga have since withdrawn from a string of other towns, including Khanaqin and Jalawla in Diyala province and Makhmour, Bashiqa, Sinjar and other areas in Nineveh province, the Iraqi military statement said.
Kurdish forces had established control over Sinjar while battling IS. The town was the site of one of the jihadist group’s worst atrocities in 2014, when thousands of Yazidis were killed and enslaved.