Speaking at a business forum in Riyadh, Mohammed bin Salman said "the crime was painful to all Saudis" but he would never allow any rift with Turkey.
The Saudis have previously denied accusations that the prince, the de facto ruler, had a role in the killing.
Khashoggi died during a 2 October visit to the Saudi consulate in Istanbul.
The Saudi government has blamed the murder on "rogue agents".
