"It is absolutely essential to have a credible investigation and to have the punishment of those that were guilty," Guterres said at the Doha Forum conference in Qatar on Sunday.
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 October 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 Mohammed bin Salman.
Despite speculation that the powerful crown prince ordered the hit, the kingdom has strongly denied he was involved.
The murder has damaged Riyadh's international reputation and Western countries, including the United States, France and Canada, have placed sanctions on nearly 20 Saudi nationals.
In addition, the US Senate voted on Thursday to approve a resolution calling for an end to US involvement in the Saudi-UAE-led military campaign in Yemen, setting the stage for a potential showdown next year between Congress and President Donald Trump over US military support for Saudi Arabia.
The Senate also approved a resolution saying that Prince Mohammed is responsible for the murder of Khashoggi.
US politicians have grown increasingly outraged as the number of civilians killed in Yemen by Saudi and UAE air attacks using US-made weapons has risen dramatically in the past two years.