Ban and Davutoglu met on the sidelines of the 70th UN General Assembly in New York, the UN spokesperson`s office said in a statement.
"The Secretary-General warmly thanked the prime minister for his country’s very generous support to the huge influx of refugees from Syria," read the statement.
A four-and-a-half year civil war in Syria has claimed more than 250,000 lives and made the country the world`s single-largest source of refugees and displaced people.
The UN refugee agency says 95 percent of the latest million Syrian refugees have gone to Turkey, which has become the world`s largest refugee-hosting country. It is home to more than 2 million registered Syrian refugees.
Ban and Davutoglu also discussed at length the situation in Syria and Iraq, including international efforts to counter the threat posed by Daesh and move toward a political solution to the Syrian conflict, according to the UN statement.
During the meeting, which was closed to media, the UN chief expressed condolences to Turkey for recent terrorist attacks that have martyred 130 security forces since July 7.
"The Secretary-General and the prime minister agreed on the importance of the negotiations for a comprehensive settlement in Cyprus, as well as Turkey’s role in supporting the process," the UN said.
Since the collapse of the joint government in 1963, Turkish Cypriots and Greek Cypriots have sought a comprehensive settlement to renew their partnership. Negotiations between the two sides to settle the decades-long conflict resumed in May after a seven-month pause.
Ban and Davutoglu "also discussed developments related to the Middle East Peace Process, especially the current need to keep tensions down in Jerusalem", the UN said.
Meanwhile, the Turkish premier`s intense diplomacy with world leaders continued Monday on the margins of the General Assembly.
He held bilateral meetings with Iraqi Prime Minister Haider al-Abadi, Lebanon`s Prime Minister Tammam Salam and Georgian Prime Minister Irakli Garibashvil during the day.
He also separately met with U.S. President Barack Obama and Russian President Vladimir Putin during a luncheon hosted by the UN chief.
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