Ankara had claimed that the entry of its forces into Iraq follows an agreement with the Iraqi government, but Baghdad has denied the claims, and called on Turkey to withdraw its forces immediately.
Iraq's powerful militias have also joined the fray, threatening to attack Turkish interests in Iraq, if Turkey did not withdraw its forces.
Zamili, who was speaking to al-Araby al-Jadeed's Arabic service, stressed the Turkish "incursion" had taken place without coordination with the Iraqi government.
"Iraq has the ability to repel these forces and drive them out of Iraqi territory. We could also request Russia to intervene militarily in Iraq in response to Turkish violation of Iraqi sovereignty," he added.
Kata'ib Sayyid al-Shuhada, one of the Shia militias of the Popular Mobilisation, has threatened to attack Turkish interests in Iraq.
"Turkish interests in Iraq will now be a legitimate target because of Turkey's assault on Iraqi territories," the militia said in a statement.
This was echoed by Harakat al-Nujaba, another Shia paramilitary group, which called on the Iraqi government to deal with Turkey as a "terrorist state".
'Baghdad consented to Turkish deployment'
However, this sentiment was contradicted by Atheel al-Nujaifi, former governor of Nineveh, of which Islamic State-held Mosul is the capital.
"The Turkish deployment had the approval of Prime Minister Haider al-Abadi personally," he said in a statement.
The former Nineveh governor claimed the Turkish forces were in Iraq to train fighters of the National Mobilisation, a force made up of mainly Sunni Arab former Iraqi police and volunteers from Mosul.
"The Turkish forces have been at the training site for months. They are non-combat forces that had entered with the knowledge and consent of the government," Nujaifi said.
Nujaifi welcomed Turkey's intervention against the Islamic State group (IS, formerly ISIS), provided that it would be part of the international coalition working to liberate the city of Mosul, as he said.
Some political experts accused pro-Iranian politicians in Iraq of coming out against Turkish deployment at the behest of Russia and Iran, linking this to the recent tensions between Moscow and Ankara.
The experts say everyone in Iraq has been aware of the Turkish presence in Nineveh for months now.
Iraq's Foreign Ministry summoned the Turkish ambassador on Saturday to demand that Turkey immediately withdraw hundreds of troops deployed in recent days to northern Iraq.
The ministry said in a statement 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 said 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.
|Turkish forces 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 labour union that was broadcast live by NTV news channel.
IS militants overran Mosul in June 2014. A much anticipated counter-offensive by Iraqi forces has been repeatedly postponed because they are tied down in fighting elsewhere.
Iraq has urged the international community to provide more weapons and training in its battle against Islamic State, but rejects most forms of direct intervention, mistrusting the intentions of foreign powers.
Davutoglu said the camp, located some 30 kilometres northeast of Mosul, was set up at the Mosul governor's request and in coordination with the Iraqi Defence Ministry.
"It has trained more than 2,000 of our Mosul brothers, contributing to the freeing of Mosul from the Islamic State terrorist organisation," he said.
Iraqi President Fuad 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 defence 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 Shia Muslim 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.