The polls were due to be closed at 6pm local time (15:00 GMT) but the Kurdish Regional Government's Election Commission extended the operation by another hour.
In the oil-rich city of Kirkuk, The Guardian reported, Kurdish neighborhoods were teeming with voters, many wearing traditional costumes. "We are registering them on a daily basis and ready to register them through September 24", he said, explaining it was unexpected for this number of internationals to come and observe the referendum process.
Many oppose the vote, including the US, the European Union and Turkey, as well as Iraq's central government in Baghdad, which claims some of the same oil-rich territory as the Kurds. Final results are expected within 72 hours.
The vote organised by Kurdish authorities is expected to deliver a comfortable "yes" for independence, but is not binding.
"What is the Kurdish population of northern Iraq?"
"The Secretary-General respects the sovereignty, territorial integrity and unity of Iraq and considers that all outstanding issues between the federal Government and the Kurdistan Regional Government should be resolved through structured dialogue and constructive compromise", his Spokesman, Stéphane Dujarric, said in a statement.
Kirkuk residents also flocked to polling stations of the ethnically-mixed city to cast their votes.
"Parliament demands that the head of the army (Prime Minister Haider al-Abadi) deploy forces in all of the zones the autonomous region of Kurdistan has taken control of since 2003", a resolution said.
Turkey took the Kurdish television channel Rudaw off its satellite service TurkSat, a Turkish broadcasting official told Reuters, in the country's first response to a Kurdish independence referendum that began on Monday in northern Iraq.
Iraqi Kurds were voting on Monday in defiance of warnings from Ankara as well as Baghdad and Iran.
The curfew was announced in statement from the Kurdish-led governorate of the northern Iraqi city.
Turkey, Iran, the U.S. and the United Nations have warned that the vote might derail operations against Daesh and lead to greater instability in the region.
The referendum has been condemned by the USA, Iran, Turkey and a number of other countries, as well as the countries of the Arab League.
President Barzani has said a "Yes" outcome would not result in an automatic declaration of independence, but would lead to further negotiations with Baghdad.
Voting started on Monday in northern Iraq despite intense global and regional pressure to call the vote off.