Those who did take part showed off their ink-stained fingers after casting their vote.
“If I had 20 fingers, I would have voted 20 times for my state,” Ibtissam Mohammed, 45, said.
Kirkuk governor Najm Eddine Karim, who was fired by Baghdad after his provincial council decided to take part in the poll, also voted.
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.
“I don’t want separation from Iraq, violence or war,” she said.
– ‘Necessary measures’ –
Left without a state of their own when the borders of the Middle East were redrawn after World War I, the Kurds see themselves as the world’s largest stateless people.
The non-Arab ethnic group number between 25 and 35 million people spread across Iraq, Iran, Turkey and Syria.
Iraqi Prime Minister Haider al-Abadi on Sunday pledged to take all the “necessary measures” to protect the country’s unity as his government urged all countries to deal only with it on oil transactions.
Abadi said the Kurds’ unilateral decision to stage a referendum affected both Iraqi and regional security, and was “unconstitutional and against civil peace”.
Hours later, the Iraqi government called on all countries “to deal only with it on matters of oil and borders”.
The Iraqi Kurds export an average 600,000 barrels per day (bpd) through a pipeline running through Turkey to Ceyhan on the Mediterranean.
Turkey’s President Recep Tayyip Erdogan on Monday threatened to halt these oil exports, angrily denouncing an “illegitimate” referendum.
He also said Turkey’s Habur border crossing with Iraqi Kurdistan would be closed.
Turkish Prime Minister Binali Yildirim earlier said sanctions could also be “with regard to air space”.
Tehran closed its border with Iraqi Kurdistan after saying on Sunday it had blocked all flights to and from the region at Baghdad’s request.
Iranian news agency IRNA said Iran’s President Hassan Rouhani had called Abadi late Sunday to reiterate his support.
But Barzani said the Kurds’ “partnership with Baghdad” since the ouster of dictator Saddam Hussein in a 2003 US-led invasion had failed.
He however said the vote was “not for defining borders or imposing a fait accompli”.
“We want a dialogue with Baghdad to resolve the problems, and the dialogue can last one or two years,” Barzani said of zones such as Kirkuk.