The vote in the autonomous Kurdish region of northern Iraq and some disputed areas is non-binding and will not lead automatically to independence, but is seen by the Kurds as a major step towards a long-cherished dream of statehood.
Voters flocked to the polls, eager to show off their ink-stained fingers after casting their ballots, and an overwhelming "Yes" outcome is expected.
Turnout was 72 percent, with 3.3 million of the 4.58 million registered voters taking part, election commission spokesman Shirwan Zirar said late Monday.
Prior to the vote, the commission had put the electorate at 5.3 million.
The vote took place peacefully and in a festive atmosphere, but signs of potential trouble mounted as the day progressed, with Washington saying it was "deeply disappointed" that the ballot went ahead.
"The United States' historic relationship with the people of the Iraqi Kurdistan Region will not change in light of today's non-binding referendum, but we believe this step will increase instability and hardships for the Kurdistan region and its people," State Department spokeswoman Heather Nauert said in a statement.

Some five million Kurds took to the polls across three provinces in the historic independence referendum. Source: AAP
UN concerned
In New York, UN chief Antonio Guterres also expressed concern about the "potentially destabilising effects" of the referendum.
Expressing respect for "the sovereignty, territorial integrity and unity of Iraq", he called for differences to be resolved through "structured dialogue and constructive compromise".
Lawmakers in Baghdad, which has declared the vote unconstitutional, demanded the government send troops to disputed areas where the referendum was taking place.
In Istanbul, President Recep Tayyip Erdogan warned that Turkey - which fears the effects of the vote on its own sizeable Kurdish population - would shut its border with Iraqi Kurdistan and threatened to block key exports.
And in Kirkuk, a disputed city where the vote controversially went ahead, security forces deployed on the streets after a curfew was imposed in parts of the city.
'Day of celebration'
Soon after voting began in the Iraqi Kurdish capital Arbil, many men headed to polling stations dressed in traditional Kurdish dress of brown shirt and billowing trousers for the occasion.
"I came very early to be the first to vote for a Kurdish state," said Diyar Abubakr, 33.
"It's a day of celebration today. That's why I've put on our traditional outfit, which I bought for the occasion."
One voter even brought a cow to slaughter before the start of the referendum.
"I brought this cow as today the state is born and it's tradition to slaughter a cow for a birth," said Dalgash Abdallah, 27.
Veteran Iraqi Kurd leader Massud Barzani, who initiated the vote, cast his ballot early in the morning, smiling and wearing a traditional outfit.
He pushed ahead with the referendum despite the opposition from Baghdad and Ankara, but also from Iran which has its own large Kurdish population, and Western countries who fear the vote could hamper the fight against the Islamic State group in which cooperation between Baghdad and the Kurds has been key.
Polling stations were scattered across the three northern provinces of autonomous Iraqi Kurdistan - Arbil, Sulaimaniyah and Dohuk - as well as in disputed border zones such as the oil-rich province of Kirkuk.
In Sulaimaniyah, second city of the autonomous region, 40-year-old Diyar Omar came to vote also wearing traditional clothes.

A man casts his referendum vote at a polling station in the city of Erbil, the capital of the autonomous Kurdish region of northern Iraq. Source: AAP
"We will seize our independence through the polls," he said.
"I'm so happy I could take part in this independence vote during my lifetime."
A total of 12,072 polling stations were open for more than 5.3 million registered voters.
As voting progressed, Iraq's parliament ordered Prime Minister Haider al-Abadi to "deploy forces" in areas disputed with the Kurds.
Asked about the risks of armed conflict, Abadi's spokesman Saad al-Hadithi told AFP: "If there are clashes in these zones, it will be the job of federal forces to apply the law."
Karim al-Nuri, a head of the Badr Brigade which forms part of the powerful Hashed al-Shaabi paramilitary units, suggested the group was ready to deploy to "Kirkuk and the disputed zones occupied by armed gangs, outlaws
Curfew in Kirkuk
Kirkuk, home to Arabs, Kurds and Turkmen, has been a particular point of concern and late on Monday police said a curfew was being imposed in the centre of the city and in Arab and Turkmen areas "to ensure security, monitor the situation and protect the citizens of Kirkuk".
A senior official in Kirkuk later said the situation was stable and that the curfew would be lifted within hours.
"Tomorrow will be a normal work day in Kirkuk," he said.
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.
The Iraqi Kurds export an average 600,000 barrels per day through a pipeline running through Turkey to Ceyhan on the Mediterranean.
Erdogan on Monday threatened to halt these oil exports, angrily denouncing an "illegitimate" referendum.
Erdogan also said Turkey's Habur border crossing with Iraqi Kurdistan would be closed.
He again urged Iraqi Kurdish authorities to take a step back and appeared to threaten a possible cross-border operation.
"In Iraq, when necessary, we will not shy away from taking these types of steps," Erdogan said, referring to Turkey's military operation launched last year in Syria against IS and Syrian Kurdish militia.
However, the referendum sparked celebrations in the Syrian Kurdish city of Qamishli, in solidarity with their brethren across the border.
"We've been waiting for this moment for more than 100 years, to celebrate the independence of Kurdistan," said one of the revellers, Rezkar Pigeot, 40, as young Kurds sang and danced in the streets.
Tehran has also increased pressure, announcing on Sunday it had blocked all flights to and from the region at Baghdad's request.
The foreign ministry in Tehran said its land border with Iraqi Kurdistan remained opened however, reversing an earlier statement.
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.
TV channels removed
Meanwhile Turkish authorities on Monday ordered the removal of three Iraqi Kurdistan-based TV channels from Turkey's main satellite operator, on the same day as a controversial independence vote in the autonomous region, local media reported.
Broadcasting watchdog RTUK ruled that Rudaw -- a channel considered close to Iraqi Kurd leader Massud Barzani -- Kurdistan 24 and Waar TV, should be removed from Turksat, Dogan news agency reported.
RTUK's decision was made in an extraordinary meeting on Monday because the channels are "not based in Turkey and do not have a broadcasting licence", the agency said.
According to Dogan, the decision was carried by RTUK members from the ruling Justice and Development Party (AKP) and opposition far-right Nationalist Movement Party (MHP).
Neither the main opposition Republican People's Party (CHP) nor pro-Kurdish Peoples' Democratic Party (HDP) members attended the meeting because they were "out of town", the agency added.
The HDP decried the "utterly political decision that is not legal" in a statement on its website, accusing RTUK of being pressured by the government.