The appeal from the Kurdistan regional government came after the Turkish parliament authorised its army to cross into Iraq to crack down on rebels from the Kurdistan Workers' Party (PKK).

"The KRG welcomes direct dialogue with Ankara on all issues of common interest or concern, including the PKK," said a statement from Iraq's autonomous Kurdish entity.

"An incursion would be detrimental to all Iraq, to Turkey and the Middle East," the administration said in the statement posted on its website.

Several thousand Iraqi Kurds took to the streets of their regional capital Arbil and the border town of Dohuk, holding aloft the red, white and green Kurdistan flag that is banned in Turkey.

"No no for the Turkish threat, yes yes for peace," shouted some of the several thousand protesters in Arbil who carried banners written in Arabic, Kurdish and English.

"We demand that the Iraqi government and international community stand together against the Turkish threat," said one banner. "Violation over the Kurdistan border is a violation of the people of Kurdistan," said another.

Protected by tight security that cordoned off the centre of Arbil to traffic, the protestors handed over a letter to the UN official.

"The best way to treat the PKK issue is to hold a dialogue between the Turkish leadership and the Kurdish leadership," said Karim Ali, a 21-year-old student draped in a Kurdish flag.

"Why are they threatening us?" he asked. "We are not a part of the PKK issue."

One protestor accused the Turks of having a hidden agenda that was targeting Iraqi Kurdistan, not just the PKK rebels.

"As big as this demonstration is, I think it will not be any use because the Turkish have decided to destroy the Kurdistan experiment," said Ahmed Salim, 19. "I don't think we can stop the Turkish threat."

Meanwhile in Dohuk, the main town on the border with Turkey, some 5,000 demonstrators gathered holding banners saying, "We condemn the Turkish threat," and calling on support from the international community.

They also held Kurdish flags and pictures of the late Mustafa Barzani, a Kurdish nationalist leader and the father of Massoud Barzani, the current president of the Kurdistan region.

Barzani's government implicitly denounced the actions of the rebels, who have bases in their region, condemning "the killing of innocent people in Turkey," and saying violence did not solve any problems.

Its appeal for talks, however, appeared to flout a decree from Iraqi government spokesman Ali al-Dabbagh that the PKK issue with Turkey was a matter of national security and all statements should come from Baghdad.

"The Iraqi central government is the one that will deal with this threat and all the other concerned parties should understand the central government is running this crisis and they should not make separate statements," Dabbagh said following the parliament vote in Ankara on Wednesday.

The PKK has waged a bloody campaign for Kurdish self-rule in southeast Turkey since 1984 that has claimed more than 37,000 lives.

Turkey says the rebels -- blacklisted as a terror group by both the European Union and the United States -- enjoy freedom of movement in northern Iraq and are tolerated if not supported by the regional government.

In its statement on Thursday, the Kurdish government denied it was backing the rebels and insisted Iraqi Kurdistan was a friend of Turkey's.

"We appeal to our friend and neighbour Turkey to refrain from military action in Iraq. The KRG seeks no conflict with Turkey.

"We do not and will not allow our territory to be used by anyone to attack or undermine Turkey or any of our neighbours. We do not interfere in the internal affairs of Turkey, and we expect the same in return," it said.

The regional Kurdish administration said Turkish trade and investment had been instrumental in the region's economic growth and any Turkish military attack would threaten "the fragile progress that is being made in Iraq."

During the last years of violence, Iraqi Kurdistan has largely been spared the sectarian strife and economic upheaval that has wrecked most of the rest of the country.