The Iraqi government on Tuesday demanded the "complete withdrawal" of Turkish forces from its territory, indicating Ankara's partial pullout the previous day was not enough.

Turkey deployed soldiers and tanks to a military camp in northern Iraq earlier this month, a move it said was necessary to protect trainers at the site but which Baghdad condemned as an illegal incursion.

Turkish and Iraqi officials said Turkish forces and equipment were withdrawn from the camp early on Monday, but the trainers apparently remained, and Ankara has other military sites within northern Iraq's autonomous Kurdish region.

The cabinet "renewed its firm position on the necessity of a response from neighbouring Turkey to the Iraqi demand for a complete withdrawal from Iraqi territory and respect for its national sovereignty," Prime Minister Haider al-Abadi's office said in a statement.

Turkish Prime Minister Ahmet Davutoglu said Monday that "there has been a shifting of the (military) forces, and that Ankara did "what was necessary to do from a military point of view".

But Turkish Foreign Minister Mevlut Cavusoglu indicated that forces remained at the training site, saying the number of troops there and at other locations "may increase or decrease as required".

Iraqi MP Salem al-Shabaki said Turkey had removed forces from the site near the northern city of Mosul, the main hub of the Islamic State jihadist group in Iraq, and that it seemed only trainers had remained.

The trainers have been working with anti-IS forces at the site for some time, and their presence had not previously been an issue.

The Monday withdrawal provided Abadi, who has faced intense political pressure to oppose the Turkish deployment, with a potential opportunity to declare that Ankara had met his demands.

But the wording of the latest statement indicated the government may want the trainers to be withdrawn along with Turkish forces at other sites, some of which it has occupied for over a decade.

Iraq's autonomous Kurdish region has close ties with Ankara and is unlikely to back Baghdad in such an effort.