Abadi arrived in Ankara late morning and went to the presidential palace, state broadcaster TRT reported.
He was due to meet with Turkish Prime Minister Binali Yildirim afterwards.
The visit comes after relations between the neighbouring countries were strained last year over Turkey's presence at a military base in northern Iraq.
Ankara maintained an estimated 2,000 troops in Iraq, around 500 of them were in the northern Bashiqa camp training local fighters last year ahead of the successful bid to free Mosul from the grip of the Islamic State extremist group.
Ankara had particularly criticised the inclusion of Kirkuk in the independence vote, stressing the province's multi-ethnic character, where Kurds, Arabs and Turkmens live.
Abadi's visit comes as Iraqi Kurdistan proposed today to "freeze" the results of its independence referendum and the "start of an open dialogue between the government of Kurdistan and the central government on the basis of the constitution".
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