"I am confident in saying that something like this cannot happen again in the kingdom or in any of its agencies," Faisal bin Farhan Al Saud said.
He called Khashoggi's murder a "heinous" crime.
"We have taken the actions, we have brought those people who have been implicated in the murder to court, they have faced trial, they have been sentenced," the minister said adding that the kingdom will ensure that "there can not be any lapses in authority or lapses in judgment" of the security services.
Khashoggi went missing in 2018 after entering the Saudi consulate in Istanbul. Riyadh initially denied any knowledge of the journalist's whereabouts but eventually admitted that he had been killed inside the diplomatic mission's building. The Saudi government sentenced several people over their role in Khashoggi's murder and has repeatedly denied allegations that members of the royal family were involved in the incident.