They include around 1,000 jihadists who surrendered during the battle for Hawija, the last Daesh urban stronghold in Iraq until its fall late last year, Iraqi Kurdish official Dindar Zibari told reporters.
He said 350 people detained in northern Iraq who admitted to belonging to Daesh had been transferred from the city of Kirkuk, retaken by federal forces in October, to Kurdish-run prisons.
Human Rights Watch said in December that hundreds of detainees held by the Iraqi Kurdish authorities in Kirkuk were feared to have been "forcibly disappeared".
"The names of all these prisoners were submitted to the United Nations and the International Committee of the Red Cross, but they did not inform the families of 350 people," Zibari said.
He did not specify the number of foreigners among those arrested but said some had already been sent home, including a Japanese journalist detained in 2016 on suspicion of ties to Daesh.
Security forces from the autonomous Kurdish region in northern Iraq have played a significant role in the war against Daesh.
Iraqi Prime Minister Haider al-Abadi declared victory in December in the three-year campaign by Iraqi forces to expel Daesh militants from the vast areas north and west of Baghdad.
His forces also took back disputed areas in the north from the Kurds after Baghdad rejected a controversial Kurdish independence vote in September.
Baghdad has called for detainees to be handed over to the federal government but that "should be done under the supervision of the United Nations," Zebari said.