A White House official told Reuters that the two world leaders discussed Khashoggi's killing and how to respond to it during a dinner of heads of state in Paris to mark the 100th anniversary of the World War I armistice.
The Turkish leader insisted Saturday that the 15-member Saudi delegation sent to the consulate "know very well the murderer or murderers".
Saudi Arabia has rejected Turkish requests to hand over the suspects arrested over the killing.
"The Secretary emphasized that the United States will hold all of those involved in the killing of Jamal Khashoggi accountable, and that Saudi Arabia must do the same", State Department spokeswoman Heather Nauert said in a statement. And on Monday, a Turkish official said Saudi Arabia sent two experts to Istanbul with the specific aim of covering up evidence after the murder.
The foreign ministry said Hunt would meet Saudi Arabia's King Salman, Prince Mohammed, Abu Dhabi Crown Prince Sheikh Mohammed bin Zayed Al Nahyan, Saudi Foreign Minister Adel al-Jubeir, Yemeni Vice President Ali Mohsen and Foreign Minister Khaled Al Yamani.
Cavusoglu said it is clear, though, that a 15-man team alleged to have traveled to Turkey to act as a hit squad would not have taken such action on their own, and that investigators need to find who would have given that order.
Khashoggi, who lived in Virginia and wrote columns for The Washington Post, was killed when he went to the consulate in Istanbul on October 2 to pick up a paper necessary to facilitate his wedding.
Though details of the recording had previously been leaked to the media, this was the first official confirmation of its existence.
Gina Haspel, the director of the Central Intelligence Agency, flew to the Turkish capital, Ankara, last month to meet with her Turkish counterparts.
Khashoggi, a Washington Post columnist who was critical of the Saudi government and its Crown Prince Mohammad bin Salman, vanished from the Saudi consulate on October 2.
They include the killing itself and conversations pre-dating the operation which Turkey subsequently uncovered, the sources said. Khashoggi was said to be dismembered and his remains have yet to be found.
Prince Turki Al-Faisal, Saudi Arabia's former spy chief, says the country is proud of its judicial system and will never accept an global investigation into the killing of Saudi journalist Jamal Khashoggi.