The overnight announcements in Saudi state media came more than two weeks after Khashoggi, 59, entered the Saudi Consulate in Istanbul for paperwork required to marry his Turkish fiancée, and never came out.
Saudi intelligence officials have reportedly been dismissed in the aftermath of his disappearance on October 2.
Associated Press quoted Saudi state-run media as saying that King Salman has a proposal to restructure kingdom's intelligence services after the Khashoggi killing.
Oct 8: Turkish authorities summon the Saudi ambassador and ask for proof that Mr Khashoggi left the consulate.
Saudi Arabia said on Saturday a missing journalist had died in a fight inside its Istanbul consulate and it had fired two senior officials over his death, an account President Donald Trump said was credible but USA lawmakers found hard to believe.
"Saudi Arabia has been a great ally, they've been a tremendous investor in the United States", Trump said, adding, "That's why this is so sad".
The Saudi public prosecutor didn't disclose details on the whereabouts of Khashoggi's body or who was involved in the altercation.
According to CNN, five high-ranking Saudi officials have been fired, and 18 other Saudis have been arrested and are still being detained.
In an off-record interview to Newsweek magazine prior to his death - which was published on Saturday - Khashoggi described Qahtani and another Saudi top official Turki al-Sheikh as "thuggish".
Saudi state media confirms Khashoggi died in Istanbul consulate
An official familiar with the Saudi operation said: 'There were no orders for them to kill him or even specifically kidnap him. The state media also reported that two high-ranking Saudi officials have been fired by King Salman , including Maj.
Should Chelsea fans be concerned about David Luiz ahead of Manchester United?
"We also had surprises with players that we had no idea that they were injured and they arrived with important injuries". He added: "We are talking about a coach that has won everything, everywhere, so I think you have to respect him".
Facebook has hired Nick Clegg to lead its global affairs
The former MP had reportedly spent months trying to woo Facebook Chief Executive Mark Zuckerberg. Clegg will succeed Elliot Schrage, who announced his departure from Facebook in June.
It's also an about-face from the kingdom's previous denials of any involvement in Khashoggi's October 2 disappearance at the consulate.
Turkish officials have said Khashoggi was killed and dismembered.
Trump has continued to balk at suggestions that the USA halt arms sales to Riyadh, saying earlier Friday that doing so "would be very hurtful to this country" and adding after the Saudi explanation was made public he "would prefer we don't use as retribution cancelling $110 billion worth of work".
Trump's previous warnings over the case drew an angry response Sunday from Saudi Arabia and its state-linked media, including a suggestion that Riyadh could wield its oil production as a weapon.
"The new explanation is preposterous, and America's moral compass has come completely unmoored if we don't take action", Murphy said in a tweet. "But at the same time, the brash and abrasive young innovator has not encouraged or permitted any popular debate in Saudi Arabia about the nature of his many changes", Khashoggi wrote in the British daily The Guardian in March.
President Donald Trump, speaking at a defense roundtable in Arizona on Friday night, called the Saudi report a "good first step".
However the mission is said to be led by his son Crown Prince Mohammed bin Salman, who was suspected of being behind Khashoggi's disappearance in some versions of stories alleging what happened to the Washington Post writer.
Those having such links will be held accountable and brought to justice, it added.
In an article published in the Post a year ago, Khashoggi, whose 60th birthday was on October 13, said that under Prince Mohammed - the kingdom's de facto ruler - Saudi Arabia was entering a new era of "fear, intimidation, arrests and public shaming".