Iraq's top Shiite cleric Grand Ayatollah Ali al-Sistani on Friday criticised the deployment of Turkish troops and tanks to the country's north that Baghdad says took place without its approval.

Top Turkish officials said a deal had been reached with Baghdad over the forces, which were sent to a base near the city of Mosul, but Iraq reiterated demands that Ankara's troops be withdrawn and called on the United Nations to take action.

No country should "send its soldiers to the territory of another state under the pretext of supporting it in fighting terrorism without the conclusion of an agreement... between the governments of the two countries," Sistani said in remarks delivered by a representative at weekly Friday prayers.

Sistani is revered by millions and his words carry significant weight with Iraq's Shiite majority and politicians.

Turkey has been training forces opposed to the Islamic State jihadist group, which overran large areas north and west of Baghdad last year, at the base where the recently deployed troops were sent.

Turkish Prime Minister Ahmet Davutoglu has defended the deployment 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 gives 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 also sought to expand its presence.

Turkish President Recep Tayyip Erdogan said Friday that the forces should remain "within an agreement" with Iraqi authorities and that a delegation sent to Baghdad "returned with this agreement", but did not specify the nature of the deal or with whom it was made.

Davutoglu's office also said that the two sides had reached an agreement on the "reorganisation" of the Turkish troop presence.

- 'Turkish incursion' -

But remarks from the Iraqi side did not point to an accord, with Prime Minister Haider al-Abadi saying Friday that he had directed the foreign ministry to make a "formal complaint" over "the Turkish incursion".

He also called on the UN Security Council to "protect Iraq and its security, sovereignty, safety and territorial integrity, which were violated by Turkish forces", a statement from his office said.

Abadi, whose high-profile reform programme has accomplished little in the way of lasting change, can ill afford another setback now.

Turkish Foreign Minister Mevlut Cavusoglu took a more conciliatory tone on Friday, saying that "it is our duty to address the Baghdad government's concerns".

But he also indicated that Ankara wanted to obtain Iraqi approval for the deployment.

"Especially after starting the fight against (IS), threats have increased against Turkey and our forces on the ground. It is the Turkish republic's duty to ensure our troops' security," Cavusoglu said during a live interview on NTV television.

IS "still controls around 35 percent of Iraqi territory. Do you (Iraq) have a force to ensure security of our troops providing training there? No. Then who will protect them? We are discussing this," he said.

Earlier this week, Iraq gave Turkey 48 hours to remove the forces, but the deadline passed without Ankara doing so and Erdogan on Thursday ruled out a withdrawal.

"What they do in Bashiqa and at the camp is training," Erdogan told a news conference in Ankara, referring to the area where the base is located.

"The number of our soldiers will increase or reduce according to the number of peshmerga (Iraqi Kurdish forces) who are trained. (Their) withdrawal is out of the question," he said.