"It is absolutely essential to have a credible investigation and to have the punishment of those that were guilty," Guterres said at a conference in Doha, AFP reported.
The UN chief said he had no information on the case except what had been reported in the media.
Khashoggi, a Saudi contributor to the Washington Post, was killed on Oct. 2 shortly after entering the kingdom's consulate in what Riyadh called a "rogue" operation.
Saudi Arabia has repeatedly rejected Turkish demands to extradite suspects connected to the murder of the journalist, a critic of Crown Prince Mohammad bin Salman.
Turkey's foreign minister said Saturday that his country would "not give up" on establishing the truth about the murder.
"We haven't received any new information or outcome of the investigation from the Saudi side," Mevlut Cavusoglu said.
"Turkey will not give up on this, we will go to the end."
Earlier this month, the minister said Turkey was in talks over a possible United Nations investigation into the killing which has provoked global outrage.
According to Turkey, a 15-member Saudi team was sent to Istanbul to kill Khashoggi, a palace insider turned critic of the regime.
Riyadh has since detained 21 people over the murder.
Despite speculation that the powerful crown prince ordered the hit, the kingdom has strongly denied he was involved.