The announcement underscored the rapidly mounting pressures on Saudi Arabia to fully illuminate Khashoggi's killing, after its previous explanations were contradicted by Turkey and met with skepticism by the United States, a close Saudi ally.
The affair prompted numerous high-profile political and business leaders to pull out of Saudi Arabia's Future Investment Forum (FII) in the capital Riyadh this week.
"Whether or not they acted in the name of the state, that remains to be discussed and investigated", she said.
A person familiar with the recording who spoke to the Post called the audio "compelling" and said it would likely further pressure USA officials to respond forcefully against the Saudis for Khashoggi's death.
Saudi Arabia's pro-government Okaz newspaper said Salah - a dual US-Saudi citizen - departed the kingdom on Wednesday, without offering any details.More news: 'Luke Cage' Actor Mike Colter Reacts to Netflix Series Being Canceled
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Saudi state news agency SPA said on Thursday that Prince Mohammed had presided over the first meeting of a committee to carry out that restructuring.
Turkey did not have "any desire" to take the case to an worldwide court, he added, but would be willing to share information and the outcomes of its investigation.
At a conference in Riyadh on Wednesday, the crown prince said the killing was a "heinous crime that can not be justified" and warned against any efforts to "manipulate" the crisis and drive a wedge between Saudi Arabia and Turkey, which are regional rivals but also diplomatic and business partners.
However, even US President Donald Trump has cast doubt on MBS's claim he had nothing to do with Khashoggi's murder.
Turkey has long dismissed the Saudi assertion of an accidental death and has pressed the kingdom to concede that Khashoggi was deliberately targeted for death.
First of all, the crime was really painful to all Saudis, and I believe it is painful to every human in the world.
France has said it will consider sanctions against Saudi Arabia if its intelligence services find Riyadh was behind Khashoggi's death.
At one summit session, Saudi energy minister Khalid Al-Falih described Mr Khashoggi's slaying as "abhorrent".