Salman also affirmed the kingdom's "solid" ties with Turkey, saying no one could undermine the relationship between the two countries, the Saudi foreign ministry said.
He said that allegations about orders to murder Khashoggi were "lies" targeting the government, according to the official Saudi Press Agency.
Here is a look at what we know about the disappearance.
Khashoggi is a longtime Saudi journalist, foreign correspondent, editor and columnist whose work has been controversial in the past in the ultraconservative Sunni kingdom.
Khashoggi, who was considered close to the Saudi royal family, had become a critic of the current government and Prince Mohammed, the 33-year-old heir apparent who has shown little tolerance for criticism.
Yemeni Nobel Peace Prize laureate Tawakkol Karman (center) joins a demonstration outside the Saudi consulate in Istanbul earlier earlier this month.
Mohammed Zidan, market strategist at Thinkmarket in Dubai, said the drop in Saudi stocks was the result of panic selling because of several political and economic factors.
Still, he was careful to hedge his language - as he has been largely since Khashoggi vanished after the journalist's visit to the Saudi consulate in Istanbul. He was told to return to the consulate on October 2 to pick up those documents, Cengiz says.
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The couple, who are to Wednesday at Windsor Castle this Friday (12 October), will have a red velvet and chocolate wedding cake. Eugenie also revealed that her older sister will be with her every step of the way, as her chosen maid of honor.
Surveillance footage later aired on Turkish state television shows Khashoggi walking into the consulate at 1:14 p.m. on October 2. Media and tech companies including Uber, Virgin and Viacom have withdrawn in protest at Khashoggi's alleged killing.
Authorities recovered the audio from Khashoggi's iPhone and his iCloud account, the newspaper said. Turkish officials told The Associated Press one of those men was an "autopsy expert".
Upon noticing the watch, Khashoggi's assailants tried to unlock the Apple Watch with multiple password attempts, ultimately using the journalist's fingerprint to unlock the smart watch.
There was already mounting concern over civilian deaths caused by a Saudi-led military coalition in Yemen and some lawmakers have said Washington should block military sales to Riyadh if the allegations over Khashoggi are proven.
Soon, Turkey began leaking its suspicions to the media.
The Saudis have come under considerable worldwide pressure over the disappearance.
Imposing any type of sanctions on Saudi Arabia by the West will cause the kingdom to resort to other options, US President Donald Trump had said a few days ago, and that Russian Federation and China are ready to fulfill Riyadh's military needs among others.
Kudlow said Sunday as to whether Mnuchin would go forward with the trip, "Again, along with the president and the general investigation, Mr. Mnuchin will make up his mind as the week progresses and as new information surfaces", Kudlow said on ABC's "This Week with George Stephanopoulos".