Otaibi returned to Riyadh on Tuesday ahead of a planned search of his residence as part of the official Turkish probe into Khashoggi's disappearance.
Overnight, Turkish police completed a search of the consulate after being allowed in by Saudi authorities.
Turkish officials have said they believe Khashoggi was murdered and his body removed, which the Saudis have strongly denied.
What has come out of the Pompeo meeting?
Pompeo said that in his talks Tuesday with Saudi leaders, he stressed the importance of an investigation whose results can be publicly aired.
"The king firmly denied any knowledge of it", Trump told reporters as he left the White House for a trip to survey hurricane damage in Florida and in Georgia.
The president later told reporters: "The denial was very, very strong".
"Well he wasn't a citizen of this country for one thing", Mr. Trump said.
Mr Pompeo is expected in Turkey later. "If they knew about it, that would be bad". "Saudi Arabia literally has a sword on the flag, so you know". President Trump is also correct when he says thousands of U.S. jobs would be lost, with China and Russian Federation to be among those lining up to replace them.
There are claims that Mr Mr Khashoggi was killed and dismembered inside the building by a 15-member Saudi "assassination squad".
A Saudi official, not authorized to speak publicly, told Reuters that the king had ordered an internal investigation based on information from the joint team in Istanbul.
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One of the men appears to be bodyguard Maher Abdulaziz Mutreb, a regular member of Crown Prince Mohammed bin Salman's entourage.
What are U.S. media reporting?
Khashoggi went missing after entering the Saudi consulate in Istanbul earlier this month. Trump has speculated without providing evidence that "rogue killers" could be responsible.
Gardiner says Iran, a regional rival to Saudi Arabia, comes into play as well.
Members of Khashoggi's family called for an investigation, in a statement released on Monday.
How was the consulate search conducted?But this is the first time Turkish media has claimed to hear the tapes.
President Recep Tayyip Erdogan said today he hoped a "reasonable opinion" would be reached as soon as possible, clarifying what happened when the Saudi journalist entered his country's consulate in Istanbul two weeks ago.
What allegedly happened in Istanbul?
Khashoggi disappeared after entering the Saudi consulate in Istanbul on October 2 to obtain documents to marry his fiancée, Hatice Cengiz.
Members of the US Congress, including some of Mr Trump's fellow Republicans, are among the loudest voices in the US demanding answers and action on Mr Khashoggi, who moved to Washington past year fearing retribution for his critical views on the Saudi leadership. This guy's got to go.
On Tuesday, a high-level Turkish official told the AP that police found "certain evidence" of Khashoggi's slaying at the consulate, without elaborating. The Saudi government didn't respond to a request for comment. He is a United States resident.