NATO will withdraw its Iraq training mission at year-end after Baghdad refused to grant it legal immunity, Iraq's top security adviser said on Sunday, mirroring the nearly-complete pullout of US forces.

But a NATO official in Brussels denied that any decision had been taken.

Iraq said the end of the mission was a surprise, with NATO previously having agreed in principle to staying through to the end of 2013.

"NATO surprised us with this decision," National Security Adviser Falah al-Fayadh said in an interview aboard a flight transporting Prime Minister Nuri al-Maliki to Washington.

"We are sorry that NATO has advised that it will withdraw its mission from Iraq... because immunity is something that is out of the government's reach," he added, saying Baghdad was informed of the decision on Thursday.

The failure to agree on immunity from prosecution closely mirrors Iraq's refusal to grant US soldiers similar protections earlier this year, sinking a potential deal between the two countries that means all American soldiers left in Iraq will leave by year-end.

Around 6,000 US troops remain stationed in the country on three bases, down from peaks of nearly 170,000 soldiers and 505 bases.

Fayadh added: "I would have preferred that there would be cooperation with NATO in other aspects, and not only through its mission in Iraq, and I was hoping that this mission would stay."

An official at NATO headquarters in Brussels, however, said: "There hasn't been a decision yet."

"When they ask us to extend the mission, we need to see that the same legal framework will extend as well," the official said on condition of anonymity.

On November 29, Iraqi government spokesman Ali al-Dabbagh said Iraq was studying a contract to extend NATO's presence in Iraq beyond year-end, but noted that such a deal would not grant its troops immunity from prosecution.

And on the same day, a NATO spokesman said the grouping had been asked by Maliki to "extend its training mission until the end of 2013."

"The North Atlantic Council (the ambassadors of the 28 NATO Allies) has accepted this request in principle. Technical details are currently being worked out," the spokesman said at the time.

Major General Jeffrey Buchanan, the spokesman for US forces in Iraq, said that Baghdad and NATO were working on an agreement that would see around 150 trainers beyond year-end. At the end of 2010, the training mission was comprised of 180 trainers.

NATO's training mission in Iraq was aimed at assisting "in the development of Iraqi security forces training structures and institutions", and as of November 2011, 12 countries were represented in its force.

Also on Sunday, US forces handed over to Iraq's defence ministry a fourth base, Contingency Operating Site Kalsu, near the central Iraqi town of Iskandiriyah, in Babil province.

Since the 2003 US-led invasion, Iraq has built up forces more than 900,000 strong, including an army that US and Iraqi officials reckon is capable of dealing with internal threats, despite the violence.

Security leaders roundly acknowledge, though, that the country is incapable of defending its borders, airspace and territorial waters.