Foreign Minister Adel al-Jubeir told Fox News the act was a "tremendous mistake" and denied the influential crown prince ordered the killing.
"We are determined to find out all the facts. And we are determined to punish those who are responsible for this murder," he said.
"The individuals who did this did this outside the scope of their authority," he added. "There obviously was a tremendous mistake made, and what compounded the mistake was the attempt to try to cover up."
"We are determined to find out all the facts. And we are determined to punish those who are responsible for this murder," he further said.
Saudi Arabia has been under pressure to explain what happened, having first said Mr Khashoggi was alive.
He was last seen entering the Saudi consulate in Istanbul on 2 October.
Turkish officials believe Mr Khashoggi, a prominent critic of the Saudi government, was murdered by a team of Saudi agents inside the building.
Saudi Arabia initially said he had left the building unharmed but on Friday admitted for the first time he was dead, saying that he was killed in a fight.
That claim though met widespread scepticism.
(Excerpts : BBC News)