The two leaders had a closed-door meeting at the Apostol Palace's Library Hall, which lasted for an hour.
Turkish Prime Minister Binali Yildirim says his visit aims to mainly address the Rohingya crisis, as well as boost relations between the two nations.
Turkish President Recep Tayyip Erdogan will discuss regional developments and Ankara's bilateral relations with Doha amid a blockade of Qatar by its Gulf neighbours.
The UN said that there was a sharp increase in arrivals this week, when hundreds of boats arrived in Bangladesh.
The UN says about 270,000 Rohingya fleeing violence in Myanmar have sought refuge in Bangladesh in the past two weeks, stretching aid efforts.
UN warns of funding shortfall as Turkey delivers first foreign aid to northwestern Myanmar, where hundreds of people have been killed and thousands have fled over the border to Bangladesh.
Last year's attempted coup in Turkey has left families struggling to cope with the loss of loved ones killed by rogue soldiers.
The centre will empower women in support of Africa's development.
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