Turkish Prime Minister Ahmet Davutoglu, in a letter to Iraqi Prime Minister Haider Al-Abadi, has promised not to "deploy more troops to Bashika till your concerns about the matter are eased".
Davutoglu on Sunday informed Haider about the military training programme in progress in Bashika, duties and activities of Turkish soldiers and current developments about the matter, Xinhua quoted the prime minister office as saying in a statement.
Davutoglu said Ankara is committed to the integrity and sovereignty of Iraq and that "Turkey will not take a step against this principle."
He said Ankara will continue to support Iraq in the fight against the Islamic State terrorist organisation.
"We want to further and deepen our coordination with the Iraqi government in the fight against terror," he said.
On Saturday, Iraq summoned the Turkish ambassador to demand an immediate withdrawal of troops from the IS-controlled city of Mosul.
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Earlier, Iraqi President Fuad Masoum rejected the Turkish move as a violation of international law and Iraqi sovereignty.
Masoum called on Turkish authorities to "withdraw its forces from Iraqi territory and to prevent recurrence of such an incident, which harms the relations between the two neighbouring countries."
Haider al-Abadi also said the presence of Turkish troops is a "serious breach of Iraqi sovereignty."
"A battalion of tanks and artillery entered the Iraqi territory, specifically in Nineveh province under the pretext of training Iraqi groups without the request or authorisation from the Iraqi federal authorities," he said.
Reports said a Turkish training battalion equipped with armoured vehicles was deployed near the city of Mosul to provide training to Iraqi paramilitary groups against IS militants.
Mosul, the capital of Nineveh province, has been under IS control since June 2014.