In a written statement, the Turkish armed forces said it had "neutralized" 70 PKK "terrorist" fighters -- 40 in northern Iraq and 30 others in northeastern Syria.
But two other Kurdish groups, which the United States is assisting in the fight against ISIS, said the strikes killed more than 20 of their fighters.
Five of those casualties were among Kurdish fighters in northern Iraq, known as Peshmerga.
Others were reported by the YPG, a Kurdish group in northern Syria.
Both groups have proven to be some of the most effective fighting forces on the ground against ISIS. Tuesday's airstrikes exposed the complicated tangle of Kurdish militant groups in the region, and the tough choices that the United States faces in its regional alliances in the battle against ISIS.
Iraq warns Turkey
The five Peshmerga fighters were killed apparently in error when Turkish warplanes carried out airstrikes at dawn on Mount Sinjar, west of Mosul, on nearby positions of the PKK, according to a spokesman for the Peshmerga ministry. Nine others were injured and transferred to a nearby hospital.
The Peshmerga released a statement blaming the strikes on the presence of the PKK group, which is usually based in Turkey. It said it has long asked the PKK to leave the Mount Sinjar area.
"One of our Peshmerga military posts is located very close to the airstrikes and was hit by mistake," Halgord Hikmat, spokesman for the Peshmerga ministry, told CNN.
The Iraqi Cabinet condemned the Turkish airstrikes in the Sinjar area, saying they were a serious violation of Iraq's sovereignty, according to a statement from the Iraqi Prime Minister's media office.
"The Iraqi government warns Turkey against repeating this unjustified transgression, which could lead to escalating steps that affect the efforts of Iraq and the international community in the war against terrorism," the statement said.
Turkish President Recep Tayyip Erdogan told Reuters that the airstrikes in Iraq were "were absolutely not an operation against the Peshmerga," according to a CNN translation.
He promised Turkey would continue to go after PKK and other militants in Iraq.
"We will continue in this path in a very committed fashion," he told Reuters.
The Pentagon said the airstrikes were neither approved by nor coordinated with the US-led coalition.
"We are deeply concerned that Turkey conducted airstrikes earlier today in northern Syria and northern Iraq without proper coordination with the United States and the broader global coalition to defeat ISIS. We have expressed our concern to the government of Turkey," spokesman Maj. Adrian J.T. Rankine-Galloway said. "These airstrikes were not approved by the Counter ISIS Coalition. ...
"Given the extraordinarily complex battle space in these areas, it is vital that Turkey and all partners in the defeat-ISIS effort coordinate their actions closely as we work together to maintain maximum pressure on ISIS and ensure the safety of all coalition personnel in theater."
YPG calls attack 'cowardly'
The YPG said Turkish planes launched a "large-scale attack" on its headquarters in Mount Karachok near Syria's border with Turkey, killing "a number of our comrades."
A YPG spokesman said later that 20 fighters were killed and 18 others wounded. But it's not clear if all the dead and injured were members of YPG, or People's Defense Units.
"We as the People's Defense Units say that this cowardly attack will not discourage our determination and our free will to fight and confront terrorism," the YPG said in a statement.
The YPG is a key component of the Syrian Democratic Forces -- backed by the United States in the fight against ISIS in Syria. Those forces have been closing in on the ISIS stronghold in Raqqa
The YPG has been supported by Russia, but Turkey considers the YPG a terrorist group.
Turkey says PKK was the target
Turkey said its operations Tuesday were targeting the PKK, which Ankara, the United States and the European Union consider to be a terror group.
For decades, Turkey has been facing a violent insurgency from the PKK -- a banned group that first took up arms in 1984 seeking an independent state for the Kurdish minority concentrated in the country's southeast.
Turkey has often suggested that the PKK and YPG operate closely, although the YPG denies such ties.
Tuesday's airstrikes were not the first time that Turkish warplanes have targeted PKK positions in Iraq and Syria.
In a statement issued via Turkey's state-run news agency, Anadolu, the Turkish general staff said the airstrikes hit PKK targets in both countries.
It described the strikes as a "counterterrorism" operation "within the scope of the international law" to prevent the PKK from sending "terrorists, arms, ammunition, and explosives" to Turkey.