The ministry said in a statement on Saturday the Turkish forces had entered Iraqi territory without the knowledge of the central government in Baghdad, and that Iraq considered such presence "a hostile act".
But Turkish Prime Minister Ahmet Davutoglu claimed the troop rotation was routine and that Turkish forces had set up a camp near Mosul almost a year ago in coordination with Iraqi authorities.
"This camp was established as a training camp for a force of local volunteers fighting terrorism," he said in a speech to a labor union that was broadcast live by NTV news channel, Reuters reported.
ISIL militants overran Mosul in June 2014. Iraq has urged the international community to provide more weapons and training in its battle against ISIL, but rejects most forms of direct intervention, mistrusting the intentions of foreign powers.
Davutoglu alleged the camp, located some 30 km (19 miles) northeast of Mosul, was set up at the Mosul governor's request and in coordination with the Iraqi Defense Ministry.
"It has trained more than 2,000 of our Mosul brothers, contributing to the freeing of Mosul from the ISIL terrorist organization," he said.
Iraqi President Fouad Massoum earlier described the deployment as "a violation of international norms and law" and called on Turkey to withdraw, echoing a statement from Prime Minister Haider al-Abadi's media office a day earlier.
A senior Kurdish military officer based north of Mosul told Reuters that additional Turkish trainers had arrived at a camp in the area overnight on Thursday escorted by a Turkish protection force.
The United States was aware of Turkey's deployment of Turkish soldiers to northern Iraq but the move is not part of the US-led coalition's activities, according to defense officials in Washington.
US officials made several statements last week on plans to send more US troops to Iraq, prompting powerful Iraqi politicians and militias to protest against the presence of any foreign troops in Iraq without explicit permission from parliament.
Powerful Iraqi armed groups have pledged to fight a planned deployment of US forces to the country. Turkey has in recent months been bombing Kurdish militant positions in northern Iraq.