The Iraqi capital of Baghdad says the movement took place without its approval.
Iraq has demanded that Ankara remove the newly-deployed forces, which were sent to a base near the city of Mosul, but Turkey has pushed for them to stay.
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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.
Turkey has been training forces opposed to the Islamic State militant 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."
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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 archfoe, Turkish Kurdish rebel group the Kurdistan Workers' Party, has also sought to expand its presence.
Iraqi Prime Minister Haider al-Abadi, whose high-profile reform programme has accomplished little in the way of lasting change, can ill afford another setback now, but repeated calls for a Turkish withdrawal have gone unheeded.
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Abadi said Friday that he directed the foreign ministry to make a "formal complaint" over "the Turkish incursion."
And he called on the United Nations 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.
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