Khashoggi disappeared after entering the Saudi consulate in Istanbul on October 2 to obtain documents to marry his fiancée, Hatice Cengiz.
A Turkish daily on Wednesday claimed it has accessed audio recordings that indicate Saudi journalist Jamal Khashoggi was tortured before he was decapitated inside Riyadh's consulate in Istanbul.
After speaking with the king, Trump floated the idea that "rogue killers" may have been responsible for the disappearance. He said the United States was working with Saudi Arabia and Turkey to figure out what happened.
President Trump said on Wednesday that he doesn't want to sever ties with Saudi Arabia because they have a "tremendous order" for weapons that could potentially create a half a million jobs, until facts are established on USA resident Jamal Khashoggi.
As he dispatched Pompeo to Riyadh on Monday, Trump told reporters at the White House that King Salman's denials to him about Khashoggi's fate in a phone call "could not have been stronger".
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Pompeo was on a brief visit to Turkey after having met with the Saudi king, crown prince and foreign minister in Riyadh on Tuesday.
Trump also said "that would be bad" if Saudi Arabia's king and crown prince knew about the suspected killing of Khashoggi in the Saudi consulate.
Turkish officials believe Mr Khashoggi was murdered by Saudi agents but the Saudis have denied this. Their search included the roof and garage, and employed a drone to surveil the premises.
In the recording, Salah Muhammad al-Tubaigy, identified as the head of forensic evidence in the Saudi general security department, was one of the 15-member squad who arrived in Ankara earlier that day on a private jet.
"Yesterday evening, unfortunately, police could not search the Saudi consul's residence".
President Trump has previously said he does not want to halt a proposed $110 billion arms sale to Saudi Arabia - as some in Congress have suggested - because it would harm the USA economically.
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It is unclear whether a Saudi statement would be released, and its content hasn't been completed, the people familiar with the matter said.
The recordings reportedly suggest Khashoggi was killed in less than 10 minutes.
Though the Khashoggi case has dominated his talks so far, Pompeo has raised other issues on his last-minute trip.
"I think we have to find out what happened first", Trump told the Associated Press in an interview on Tuesday. "Here we go again with, you know, you're guilty until proven innocent. I don't like that". But one thing is certain: whatever narrative emerges, the global reputation of the Saudi Crown Prince and power-behind-the-throne Mohammed Bin Salman will forever be tainted by this affair.
Khashoggi, a familiar face on Arab talk shows, moved to the United States previous year fearing retribution for his criticism of Prince Mohammed, who has cracked down on dissent with arrests.
Concern over Khashoggi's disappearance has prompted media organizations and a growing number of guests to pull out of a "Davos in the Desert" investment conference set for October 23-25, which has become the biggest show for investors to promote Prince Mohammed's reform vision.
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U.S. Sen. Todd Young (R-Ind.) called for the suspension of arms sales, as well as for Treasury Secretary Steven Mnuchin to drop out of a Saudi investment conference in Riyadh scheduled for next week.