Voting closed at 6pm local time (16:00 GMT) on Monday, and the final results are expected to be announced within 72 hours.
In Sulaimaniyah, second city of the autonomous region, 40-year-old Diyar Omar came to cast his vote also wearing traditional clothes.
But in Khanaqeen, another disputed territory in Diyala province, Um Ali, 30, said she feared the outcome of the vote and its consequences for her and her children.
Iraq and other neighbours of the Kurds "have to understand that we have done this step by step", Bayan Sami Abdul Rahman told Al Jazeera.More news: Megyn Kelly shows a softer side on 'Megyn Kelly Today' debut
The BBC says Kurds are the fourth-largest ethnic group in the Middle East.
A few hours earlier, Iraqi Prime Minister Haidar al-Abadi emphasized that the consultation is a divisive plan of the nation and ratified that he will not recognize the plebiscite and will take measures to maintain national unity.
Bayan Sami Abdul Rahman, KRG representative to the United States, says that while the result is non-binding for the Iraqi government, it is "binding" for the Kurdish leadership "to follow the will of the people".
Iran upped the pressure on Sunday, announcing it had blocked all flights to and from Kurdistan at Baghdad's request. CHP leader Kemal Kılıçdaroğlu urged Prime Minister Binali Yıldırım to act in a "cool-headed manner" in a meeting also attended by Nationalist Movement Party (MHP) leader Devlet Bahçeli, Parliament Speaker İsmail Kahraman and deputy group leaders late September 23.More news: Kim Jong Un says he will 'tame the mentally deranged U.S. dotard'
But Barzani said the Kurds' "partnership with Baghdad" since the ouster of dictator Saddam Hussein in a 2003 US-led invasion had failed.
The US, which has deployed a contingent of military forces to a base in the Kurdistan Region, has also opposed the referendum.
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