Kurdish forces and militants of the Islamic State have battled each other only 40 kilometers from the Kurdish regional capital of Irbil.
The August 6 battle near Makhmur, to the southwest of Irbil, comes after a dramatic weekend offensive by militants in the north that prompted Iraq's Shi'ite-led government and Kurdish officials to reestablish military cooperation.
That cooperation includes Iraqi government air strikes in support of Kurdish Peshmerga fighters.
Iraqi state TV said a government air strike on August 6 in the militant-held northern city of Mosul killed 60 fighters of the Islamic State, formerly known as the Islamic State in Iraq and the Levant (ISIL).
The claim could not be independently verified and the area was inaccessible to most media.
On August 3, Islamic fighters seized the northern Iraqi towns of Zumar and Sinjar, sending thousands of people fleeing into the nearby mountains.
Jabbar Yawar, a Kurdish Peshmerga leader, said on August 6 that 50,000 members of Iraq's Yazidi religious minority are hiding on the mountain near Sinjar and could starve to death without immediate help.
Yazidis, who are ethnic Kurds and followers of an ancient religion derived from Zoroastrianism, are at high risk of being killed because they are viewed by the Sunni militants of the Islamic State as devil worshippers.
Also on August 6, Amnesty International warned that Iraqis displaced by the fighting were in need of urgent humanitarian assistance.
"Hundreds of civilians from Sinjar and its environs are missing, feared dead or abducted, while tens of thousands are trapped without basic necessities or vital supplies in the Sinjar Mountain area south of the city," the rights watchdog said in a statement.
Amnesty said most of them belong to the Yazidi minority.