Turkey withdrew forces Monday from a north Iraq camp where Baghdad said they were deployed without its permission, a move that may help defuse a bitter diplomatic row with Ankara.

It was not immediately clear how many soldiers were removed from the camp, where Ankara sent troops and tanks on a deployment last week it has defended as routine and necessary to protect Turkish trainers working with Iraqi forces battling the Islamic State jihadist group.

Baghdad has sharply criticised the deployment, terming it an "incursion" that violated the country's sovereignty, repeatedly demanding the forces be withdrawn and complaining to the United Nations Security Council.

"There has been a shifting of the (military) forces," Turkish Prime Minister Ahmet Davutoglu said of the withdrawal during a live interview with A Haber TV.

"We did what was necessary to do from a military point of view," he said, without providing details.

Iraqi lawmaker Salem al-Shabaki also said that Turkey withdrew troops from the camp near the northern city of Mosul, IS's main hub in Iraq.

"The Turkish army withdrew from Camp Zilkan at dawn today, and according to our information, only the trainers remain to train Hashad al-Watani forces," Shabaki said, referring to anti-IS volunteers.

"Witnesses confirmed that they saw the Turkish army withdrawing from Camp Zilkan... toward the Turkish border," Shabaki said.

Turkish Foreign Minister Mevlut Cavusoglu said the number of troops deployed in northern Iraq may fluctuate.

"The number of our soldiers in Bashiqa and in north Iraq may increase or decrease as required," Cavusoglu told journalists in Brussels, referring to the area where the camp is located.

That would fall short of the demands of some in the Iraqi government for a complete withdrawal from the camp.

- Heading toward border -

Turkey's state-run Anatolia news agency quoted military sources as saying that "some of the Turkish troops stationed in Bashiqa have transited to the north as part of a new arrangement".

But it did not specify if they were moving farther north into Iraq's autonomous Kurdish region, where Ankara has forces deployed at multiple sites, or leaving altogether.

Anatolia said the troops were carried in a convoy of 10-12 military vehicles but did not give further details on numbers.

Witnesses in Dohuk province in Iraqi Kurdistan reported seeing Turkish military equipment being moved on transport trucks towards the border.

"I saw these vehicles... which were carrying heavy weapons with Turkish flags on them," one witness said on condition of anonymity, but it was unclear if it was a partial or complete withdrawal.

"About six o'clock this morning, I saw transport trucks carrying tanks and armoured vehicles with Turkish flags on them going toward the Ibrahim Khalil crossing" leading from Iraq to Turkey, another witness said.

A senior Turkish official said last week that between 150 and 300 soldiers and 20 tanks were deployed to protect Turkish military trainers at the camp near Mosul.

But the deployment outraged the federal Iraqi government, which repeatedly demanded that Ankara withdraw the forces, which Baghdad said entered the country illegally.

Davutoglu defended it as an "act of solidarity" and said: "When the threats (to the trainers) increased, we sent troops to protect the camp."

But the base also gave Turkey a foothold in an area where a major ground operation against IS is eventually to take place, and where its arch-foe, Turkish Kurdish rebel group the Kurdistan Workers' Party, has sought to expand its presence.

Last week, Davutoglu sent two of the most powerful men in Turkish foreign policy -- foreign ministry under-secretary Feridun Sinirlioglu and intelligence chief Hakan Fidan -- to Baghdad in a bid to settle the tensions.

He subsequently said that an agreement had been reached on a "reorganisation" of the Turkish troops, but it was never made clear what form this would take.