"The crime was very painful to all Saudis. And it is painful, heinous to every human being in the world," Prince Mohammed bin Salman said in his first comments since the murder of the journalist.
"Those behind this crime will be held accountable... in the end justice will prevail," said during an address to the Future Investment Initiative Forum in Riyadh.
Saudi leaders have denied involvement in Khashoggi's murder inside Saudi Arabia's Istanbul consulate on October 2, pushing responsibility down the chain of command.
But the kingdom is under mounting international pressure over the killing amid US accusations of a monumental cover-up by the kingdom.
Prince Mohammed, widely known as MBS, said Saudi Arabia was working with the Turkish authorities to investigate the case.
"But they will not succeed as long as there is a king named Salman and a crown prince named Mohammed bin Salman.