However, unconfirmed reports in the United States media suggest Saudi Arabia is preparing to admit that Mr Khashoggi died as a result of an interrogation that went wrong and that the original intention had been to abduct him. The officials were not authorized to comment publicly on the matter and requested anonymity.
Turkish officials say they fear a Saudi hit team killed and dismembered the Washington Post contributor.
"There's been stark repression of anyone whose comments are not supportive of the government", he told AFP, as Saudi's public prosecutor warned earlier this week that those spreading fake news can be sentenced to five years in jail.
Turkish authorities have an audio recording indicating that Khashoggi was killed in the consulate, a Turkish official and a security source told Reuters, and have shared evidence with countries including Saudi Arabia and the United States.
Trump said Pompeo may go to Turkey after Saudi Arabia.
It is not the first time that King Salman has sought to ease tensions surrounding the 33-year-old Prince Mohammed, who has been cultivated by the USA but whose reformist credentials are being quickly shredded by the mystery surrounding Khashoggi's fate. He and Trump's son-in-law and senior adviser, Jared Kushner, have forged close ties.
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Trump has threatened the kingdom with "severe punishment" if it is shown that Khashoggi was killed inside its Istanbul mission.
But in the wake of Khashoggi's disappearance, many media and entertainment companies have been distancing themselves from the kingdom.
He has already ruled out halting a proposed $110 billion arms sale to Saudi Arabia because of the impact it would have on American jobs. At this moment there are no plans to change the Formula E calendar this season. The New York Times reported that the Saudi royal court would soon put out a narrative that an official within the kingdom's intelligence services - who happened to be a friend of Prince Mohammed - had carried out the killing.
The Washington Post reported in recent days that the Turkish government informed USA officials it was in possession of video recordings that prove Khashoggi was killed inside the consulate, but have not made them public.
Trump said he could not confirm such reports. It reported that Saba, the Yemeni news agency, said the kingdom is "being subjected to malicious and prejudicial tendencies due to its honorable and honest positions with issues regarding the Arab and Islamic nation and its leading roles in regional and worldwide stability".
King Salman and Turkish President Tayyip Erdogan spoke by telephone on Sunday evening and stressed the importance of the two countries creating a joint group as part of the probe. Surveillance footage captured him entering through the consulate's main entrance, but he was never seen leaving.
Many members of the US Congress, which has long had a testy relationship with Saudi Arabia, have issued strong criticism of the kingdom over the case.