The Iraqi government has urged Turkey to halt its military operations in the north, where Ankara has been attacking Kurdish rebel hideouts.
Turkish special forces launched Operation Claw-Tiger on Wednesday, targeting positions thought to be significant to the Kurdistan Workers’ Party (PKK), which Ankara has been fighting for decades.
Iran later carried out heavy shelling along its border in tandem with the Turkish operation, local media reported.
The Iraqi government called on Turkey to end the assault and summoned the Turkish ambassador, Fatih Yildiz, for the second time in a week.
“We stress the necessity for Turkey to stop its bombing and withdraw its aggressive forces from Iraqi territories,” Iraq’s Foreign Ministry said.
“The Iraqi government confirms that Turkey has caused heightened insecurity in the border area that is shared between us.
"We affirm our categorical rejection of these violations."
The semi-autonomous Iraqi Kurdistan region of northern Iraq is mainly Kurdish.
The Turkish Defence Ministry claimed its F-16 jets, drones and field guns had hit and destroyed more than 500 PKK targets in 36 hours.
Zagros Hiwa, spokesman for the Kurdistan Communities Union, a pan-national umbrella group founded by the PKK, said the insurgent group suffered no casualties in the attacks.
But Mr Hiwa said a civilian had been killed in Soran and two injured in Sinjar and Makhmur.
He said that strikes hit along the border area in cities such as Zakho, where there are also ground troops, and further into Iraqi territory in Sinjar, Kirkuk and the Qandil mountains, the traditional PKK stronghold.
"We call on the international community to stand against these attacks that violate international law and the basic principles that the international community works towards," Mr Hiwa told The National.
“We expect them to take practical steps against these aggressions.”
Operation Claw-Eagle, a major campaign on 81 suspected PKK targets across the region, began on Monday.
Turkey and the PKK – considered a terrorist organisation by Turkey, the US and the EU – have been fighting since 1984.
After being summoned for the first time on Tuesday, Mr Yildiz said he told Iraqi officials that if they did not take action against the rebels, Ankara would continue to "fight the PKK wherever it is".
Turkey claimed the action came after a "recent upsurge in attacks on our police stations and military bases" near the Iraqi border.
Baghdad also summoned the Iranian ambassador Iraj Masjedi to protest against Tehran's shelling of Kurdish areas.
The foreign ministry urged Iran to "respect Iraq's sovereignty and to stop these types of actions”.
"This ministry affirms Iraq is keen to maintain and develop the historical ties between the two countries, and also stresses its condemnation of these actions," it said.
Iran, which has its own minority Kurdish population, has been fighting Kurdish rebels who use Iraq as a base to mount attacks inside the country.
A spokesman for the Kurdistan Regional Government said that Turkey and Iran have continuously breached Iraq’s sovereignty.
“We have condemned their acts but nothing changes," the spokesman said.
"We spoke to the Iraqi Foreign Ministry and told of our concerns that the attacks would harm thousands of lives."
The KRG, which is ruled by the Kurdish Democratic Party, urged the ministry to hold talks with Ankara.
“We urge Iraq to review its security agreement with Turkey. We are now in negotiations with Baghdad about this,” the spokesman said.
But experts say the Turkish operation could not have taken place without the KRG's approval.
“The Iraqi government has not been able to evict Turkish troops based in camps in the Kurdistan region as there have been undisclosed agreements made between Ankara and the Kurdish Democratic Party,” said Sajad Jiyad, an analyst in Baghdad.
“There are minimal air defences in the north of Iraq and as yet Baghdad has not decided to escalate by defending or retaliating against Turkish incursions."
There has been no comment from Iraq's new Foreign Minister Fuad Hussein, a Kurd who is close to top KRG officials.
Saudi Arabia and the UAE are among those who have condemned the incursion internationally.
They called the Turkish and Iranian strikes a “violation”.
The Saudi Foreign Ministry said the kingdom considered the attacks to be “a rejected interference in an Arab country and a violation of its sovereignty”.
“The Turkish and Iranian interventions in Iraq threaten regional safety and are in violation of international principles,” it said.