The journalist disappeared after entering the Saudi consulate in Istanbul on 2 October, but the United States president said it sounded like neither the king nor Crown Prince Mohammed bin Salman had knowledge of the incident.
Earlier, US President Donald Trump said he had sent Secretary of State Mike Pompeo to Saudi Arabia and raised the possibility that "rogue killers" could be behind the disappearance of Khashoggi, who vanished after entering the Saudi consulate in Turkey almost two weeks ago.
His remarks prompted Saudi Arabia to threaten to use its economic muscle to respond to any punitive measure but Rai al-Youm, a pan-Arab newspaper based in London, said the kingdom might have to ready itself for new "milking" by the US.
Saudi Arabia has said it had nothing to do with Mr Khashoggi's disappearance, without explaining or offering evidence of how the writer left the consulate and disappeared into Istanbul with his fiancee waiting outside.
Turkish officials have accused Saudi Arabia of murdering the journalist in the building and removing his body.
Saudi Arabia has pledged to retaliate economically for any U.S. punitive action.
A Turkish diplomatic source had earlier said that a joint Turkish-Saudi team would conduct a search of the consulate - the last place that Khashoggi was seen before he vanished on October 2. "We're going to get to the bottom of it, and there will be severe punishment". Most recently Uber CEO Dara Khosrowshahi announced he will no longer be attending the event, saying, "I'm very troubled by the reports to date about Jamal Khashoggi".
But Trump, who has frequently boasted about his business ties with the kingdom, suggested during the CBS interview that ending USA arms sales to Saudi Arabia would not be an option, saying, "I don't want to hurt jobs".
Few details have emerged over how the joint working group will function, sparking suspicion that Saudi Arabia might be trying to coax Turkey with certain concessions at a time of the latter's economic problems. Germany, France and Britain also jointly called for a "credible investigation".
On Sunday, the Saudi Embassy followed up by writing on Twitter: "The Kingdom of Saudi Arabia extends...appreciation to all, including the U.S. administration, for refraining from jumping to conclusions on the ongoing investigation".
Ford Motor Co Chairman Bill Ford also pulled out, as well as media organizations like CNN and Bloomberg which once served as sponsors of the conference. "He may not", Trump said during a visit to Alabama. "There's not enough money in the world for us to buy back our credibility on human rights if we do not move forward and take swift action", Rubio said.
Khashoggi was a critic of the regime in effect led by the Bin Salman since his father appointed him crown prince in June 2017.