IRBIL, Iraq -- Iraq's prime minister on Tuesday ordered the Kurdish region to hand over control of its airports to federal authorities or face a flight ban, as the Kurds claimed victory for the "yes" vote in an independence referendum rejected by Baghdad and Iraq's neighbours.

The Iraqi Kurdish leadership billed Monday's vote as an exercise in self-determination, but the Iraqi government is strongly opposed to any redrawing of its borders, and Turkey and Iran fear the move will embolden their own Kurdish populations.

Prime Minister Haider al-Abadi issued his ultimatum a day after the landmark vote, which he said was a "historic and strategic mistake by the Kurdish leadership."

"I will not give up on the unity of Iraq, that is my national and constitutional duty," he said, adding that any ban would still allow for humanitarian and other "urgent" flights.

Masoud Barzani, the Kurdish regional president who spearheaded the referendum, called for "dialogue" with Baghdad. "Negotiations are the right path to solve the problems, not threats or the language of force," he said in a televised address.

Regional authorities in Iraq's autonomous Kurdish north put the turnout at over 70 per cent, but many voters reported irregularities, including cases of individuals voting multiple times and without proper registration. Official results are expected Wednesday.

For decades, Kurdish politics have hinged on dreams of an independent Kurdish state. When colonial powers drew the map of the Middle East after World War I, the Kurds, who now number around 30 million, were divided among Turkey, Iran, Syria and Iraq.

After polls closed in Iraq's Kurdish region Monday night, the skies above Irbil filled with fireworks and families flocked to the centre of town to celebrate. Across the border thousands of Iranian Kurds held rallies in support.

The non-binding vote is unlikely to lead to formal independence, to which virtually the entire international community is opposed, but could spark unrest at a time when Iraqi and Kurdish forces -- both U.S. allies -- are still battling the Islamic State group.

Iraqi troops are carrying out joint military exercises with Turkey along the border. Fearing the vote could be used to redraw Iraq's borders, taking a sizeable part of the country's oil wealth with it, al-Abadi has called the referendum an act of "sedition" that "escalated the ethnic and sectarian tension" across the country.

In Iran, thousands of Kurds poured into the streets in the cities of Baneh, Saghez and Sanandaj on Monday night. Footage shared online by Iranian Kurds showed demonstrators waving lit mobile phones in the air and chanting their support into the night. Some footage also showed Iranian police officers assembling nearby or watching the demonstrators.

Iranian state television on Tuesday acknowledged the rallies, a rarity in the Islamic Republic. Iran's paramilitary Revolutionary Guard and its regular army have been running military exercises near the border with Iraq's Kurdish region in a sign of Tehran's displeasure at the Kurdish referendum.

Turkish President Recep Tayyip Erdogan reiterated on Tuesday that his country is considering all options, ranging from military intervention to economic sanctions against Iraq's Kurdish region.

Erdogan said, however, that he hopes the Iraqi Kurdish leadership will abandon aims of creating a separate state and not force Turkey into enforcing sanctions.

"I hope the northern Iraqi administration gathers itself together and abandons this adventure with a dark ending," Erdogan said, adding that the landlocked Iraqi Kurdish region would not be able to survive without Turkey's support in helping export its oil.

"The moment we shut the valve it's finished for them," Erdogan said, referring to a pipeline through Turkey. The Turkish leader said no country other than Israel supports the Iraqi Kurdish referendum on independence, which he described as "invalid" and "fraudulent." He said attempts by Kurds to form an independent state are doomed to fail.

The United States and United Nations both opposed the referendum, describing it as a unilateral and potentially destabilizing move that could detract from the war Iraqi and Kurdish forces are waging against the Islamic State group.

State Department spokeswoman Heather Nauert said the U.S. wouldn't alter its "historic relationship" with Iraq's Kurds, but the referendum would increase hardships for them. She said IS and other extremists are hoping to "exploit instability and discord."

Statements from U.N. Secretary-General Antonio Guterres expressed regret that the vote was held and said issues between Iraq's federal government and Kurdish region should be resolved through dialogue.

Kurdish electoral commission spokesman Sherwan Zerar put the turnout at about 3.3 million of the eligible 4.5 million residents.

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Abdul-Zahra reported from Baghdad. Associated Press writers Jon Gambrell in Dubai, United Arab Emirates, Balint Szlanko in Irbil, Iraq and Suzan Fraser in Ankara, Turkey, contributed to this report.