Cavusoglu made the comments during a news conference in Tunis alongside his Tunisian counterpart on Monday.
He also called on Saudi Arabia to share its findings on the case with the international community.
Khashoggi was killed inside the Saudi consulate in Istanbul nearly three months ago. He entered the building on October 2 to obtain a document certifying he divorced his ex-wife so he could remarry. He was killed and dismembered inside the consulate, in what Turkey called a “premeditated murder” orchestrated by the Saudi government.
Saudi officials have countered that claim, insisting Khashoggi died in a “rogue operation”, after initially claiming he had left the building before vanishing.
In November, UN Secretary-General Antonio Guterres held talks with Cavusoglu on the killing. UN spokesperson Stephane Dujarric at the time told reporters that the UN had not yet received a formal request from the Turkish side.
In October, only weeks after the murder, four prominent rights groups – Human Rights Watch, Amnesty International, the Committee to Protect Journalists and Reporters Without Borders – urged Turkey to ask the UN to investigate the disappearance of Khashoggi.
Michelle Bachelet, the new UN High Commissioner for Human Rights, has told Al Jazeera that it is time for the UN to investigate Khashoggi‘s death – as the Saudi investigation appeared to be going nowhere.
However, Guterres, last month said he was sticking to his position that he will not act until he gets a referral from one of the UN’s major bodies and one of the member states of the UN.