A strong vote in favor of independence was expected, but the result will not be binding.
The vote was held peacefully, but the coming days could bring escalating unrest as the Kurds press ahead toward independence, something opposed by virtually the entire worldwide community, including their close ally, the United States.
Rudaw reports that after the polls close, a curfew will be imposed in Kirkuk.
Iraqi Kurds headed to the polls September 25 to vote on an independence referendum despite continued strong opposition from neighboring Turkey and Iran, the broader global community and the Iraqi central government in Baghdad.
Turkish President Recep Tayyip Erdogan is threatening a military intervention in Iraq in response to the Iraqi Kurdish region's referendum on independence from Baghdad.
He also told Iraqi Kurd authorities to ensure that the work of the United Nations mission in Iraq "will be allowed to continue unhindered".
"Iran and Turkey have warned the Kurds not to go ahead with the vote".
As voting started, Turkey said it does not recognize the referendum and will view its results as null and void.
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Kurdish officials say a "yes" vote will send a message Baghdad can not ignore, paving the way for negotiations aimed at a peaceful exit.
"The referendum "harms Iraq and harms our Kurdish brothers", Ayman Soussan added in the comments published on Monday".
Despite fears in disputed territories Iraqi territory claimed by both the Kurds and Baghdad Barzani said he didn't expect violence to follow the vote, explaining that Iraq's military and the Kurdish fighters known as the peshmerga have "good coordination in the war against terror".
Turkey is home to the largest Kurdish population at an estimated 14 million.
"The land borders between Iran and the Kurdistan Region of Iraq are open and these borders have not been closed", the ministry said, adding that only air borders between Iran and this region were now closed. "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.
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.
"The referendum does not mean independence will happen tomorrow, nor are we redrawing borders", he said in Erbil.
Barzani addressed concerns that Turkey would shut its border with the Kurdish region following the vote, saying he hoped Turkey would leave the crossing open.
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