Baghdad on Sunday welcomed Turkey's move to pull troops out of northern Iraq but said it would keep up efforts at the United Nations to achieve a full withdrawal.
"What has been reported in the media is a step in the right direction," Foreign Minister Ibrahim al-Jaafari was quoted as saying in a statement from his office.
"We will carry on our process with the (UN) Security Council until a full withdrawal is achieved," he added.
Turkey announced on Saturday that it had begun withdrawing troops in a bid to de-escalate a bitter row with Baghdad and following a call from US President Barack Obama.
"Taking into account the sensitivities on the Iraqi side... Turkey will continue the process it has already begun to withdraw its troops stationed" near Mosul, the Turkish foreign ministry said.
Earlier this month, Turkey deployed troops to a base in Nineveh province where it has a long-running training programme for forces battling the Islamic State (ISIS) millitant group.
Ankara insisted the deployment was routine and necessary to protect the trainers, while Baghdad said it was unauthorised and protested to the Security Council.
In a phone call on Friday, Obama urged his Turkish counterpart Recep Tayyip Erdogan to continue the pullout and "to respect the sovereignty and territorial integrity of Iraq".