The federal government in Baghdad has called the referendum unconstitutional.
There are concerns the vote could lead to unrest, and Washington and many Western countries have called for its postponement or cancellation, saying it will hamper the fight against the Islamic State group.
In regional capital Arbil, the political heartland of President Massud Barzani who initiated the referendum, Kurdish flags were flying everywhere.
Most people in the city said they will vote, but some also said they fear the possible consequences.
"We look forward to hearing what the situation will be after September 25, as most Kurds will vote for independence to fulfil our dream of an independent state," said labourer Ahmad Souleiman, 30.
"What we‘re afraid of is that our enemies have evil intentions towards us," he added.
Iran and Turkey have sizeable Kurdish populations of their own and fear the vote will stoke separatist aspirations at home.
Some 5.5 million Kurds are expected to vote in the three provinces that have since 2003 formed the autonomous region of Kurdistan but also in territories disputed with Baghdad such as the oil-rich province of Kirkuk.
"We all support independence because we don‘t see the benefit of staying in Iraq.
But we‘re afraid of plots by neighbouring countries," 27-year-old clothes seller Kamaran Mohammed said in Arbil.
"Today we‘re seeing neighbouring states set aside their differences to ally against us."
On Saturday, Turkish Prime Minister Binali Yildirim warned that Ankara‘s actions in response to the referendum would have "economic and security dimensions".
Asked whether a cross-border military operation was possible, Yildirim said "naturally", but "it is a question of timing as to when the security, economic and political options will be applied."
While an independent homeland has long been an aspiration in the Kurdish diaspora, the ethnic group‘s two main parties in Iraq differ on how to make it a reality.
Barzani‘s Kurdistan Democratic Party (KDP) and the Patriotic Union of Kurdistan (PUK) of Jalal Talabani are at opposite ends of the spectrum politically on the issue.
Mudah Bakhtiar of the PUK political bureau said Saturday his party "believes that the alternative (to the referendum) proposed by the UN and the major powers is acceptable".
The United States and other Western nations back a UN-supported "alternative" plan for immediate negotiations on future relations in exchange for dropping the referendum.
In Sulaymaniyah, the PUK-controlled second city of the autonomous region, enthusiasm for the vote is muted.
Hama Rashid Hassan, 51, went to a polling station on Sunday to make sure his name featured on the electoral role.
"Since I was a child, I‘ve dreamt of the day our flag appears at the United Nations," he said.
But other voters were more cautious.
"I will vote ‘no‘ tomorrow because I‘m afraid of an embargo on the region, of civil war with the Hashed al-Shaabi (grouping of Shiite paramilitaries), and waking up and seeing Turkish soldiers patrolling," said 30-year-old teacher Kamiran Anwar.
The most sensitive sticking point is Kirkuk where there was a run on food supplies in the city on Saturday as residents stocked up in case of post-referendum trouble.
On Saturday, the PUK proposed to Barzani that voting not take place in disputed areas.
MP Alaa Talabani said there would be a meeting in Arbil later Sunday on postponing the vote in Kirkuk.
Home to Kurds, Arabs and Turkmens, Kirkuk is disputed between the federal government in Baghdad and the country‘s Kurds.
The Kurds say it is historically theirs, arguing that the late dictator Saddam Hussein chased them out and replaced them with Arabs.
Threats are growing inside Iraq against the Kurdish move.
"There will be a high price to pay by those who organised this referendum, a provocation aimed at destroying relations between Arabs and Kurds," said Hashed al-Shaabi leader Faleh al-Fayad.
"As soon as the referendum takes place there will be a legal and constitutional reaction."
The Hashed grouping of paramilitary units was created in 2014 to fight against IS.
Iran-backed militia Asaib Ahl al-Haq, which comes under the Hashed umbrella, was forthright in its opposition to the referendum.
Its spokesperson urged the federal authorities to "take legal measures to confront this project that threatens civil peace and national security".
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