Turkish police believe he was killed by a special team of 15 Saudi officials, but Riyadh has dismissed the claim as "baseless".
The US chief diplomat was greeted at Riyadh airport by Saudi Foreign Minister Adel Al-Jubeir and ambassador to Washington Prince Khalid bin Salman.
Still, Saudi Arabia responded harshly, saying it would retaliate and escalate the situation if it suffered any consequences from the Khashoggi case.
US President Donald Trump speculated that "rogue killers" may be responsible. After saying yesterday that King Salman has issued a "flat denial", Trump updated that statement to say that Salman's son, the crown prince, had "totally denied any knowledge of what took place in their Turkish Consulate".
The New York Times and the Washington Post have reported, citing anonymous sources, that Saudi officials may soon acknowledge Khashoggi's slaying at the consulate but blame it on a botched intelligence operation.
Trump's attempt to distance himself from profiting from Saudi Arabia is undercut by a long record showing deals his companies made with that country's government and citizens, media reports said.
On Tuesday, a high-level Turkish official told the AP that police found "certain evidence" of Khashoggi's slaying at the consulate, without elaborating.
"Given there seems to be clear evidence that Mr. Khashoggi entered the consulate and has never been seen since, the onus is on the Saudi authorities to reveal what happened to him", Bachelet said.
Mike Pompeo, the U.S. secretary of state, has landed in Ankara for crisis talks with the Turkish president, Recep Tayyip Erdoğan, over the journalist Jamal Khashoggi as officials leaked gory details of what they claim was his murder in the Saudi consulate. The Saudi government could not be reached immediately for comment on the CNN report.
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Turkish President Recep Tayyip Erdogan told reporters the investigation "was looking into many things such as toxic materials and those materials being removed by painting them over".
In an interview that aired Sunday night, Trump threatened "severe punishment" if it turned out the Saudis did kill Khashoggi, who had been living in the USA in self-imposed exile.
Pompeo will fly to Ankara on Wednesday for talks with Turkish officials about the case.
Nils Melzer, the United Nations special investigator on torture, said that if Turkey and Saudi Arabia can't conduct "a credible and objective investigation", then global involvement may be needed.
No details have been released, but afterwards Mr Cavusoglu said they are hoping investigators will be able to gain access to the residence later on Wednesday. He said Saudi Arabia originally pledged its contribution in August, and US officials were expecting to receive it by the fall.
"This is going to alter the relationship between the USA and Saudi Arabia for the foreseeable future", Sen.
"It sounded to me like maybe these could have been rogue killers", Trump said.
The source said the timing of the two events is no accident.
"Pompeo's mission in travelling to Riyadh and then Turkey is to cover up Saudi brutality and scandal by making up stories, and this very project is an excuse to keep milking the Saudis (for weapons' contracts)", added the Javan newspaper, considered close to the Revolutionary Guards.