Reports in the United States media suggest that Saudi officials are set to admit that Mr Khashoggi was killed during an interrogation that went wrong, but neither King Salman, or his son and power behind the throne, Crown Prince Mohammed, had ordered Mr Khashoggi's death.
"The denial was very, very strong", Trump told reporters at the White House after a phone call with Saudi King Salman. After President Donald Trump on Sunday said he could take action if the allegations proved true, the kingdom threatened to use its economic clout to retaliate.
He also said Mr Pompeo would be leaving for Saudi Arabia in the next hour, adding that "we're going to leave nothing uncovered". "All they're going to do is give it to other countries, and I think that would be very foolish".
CNN's Jim Scuitto asked Jordan about Trump appearing to accept King Salman's denial at "face value".
US President Donald Trump told reporters Monday that he was aware of the report but did not know if it was correct.
The decision to dispatch Pompeo signals how much the crisis over the fate of Khashoggi, a Saudi citizen and U.S. resident who wrote critically of the kingdom's leaders, is threatening to damage USSaudi relations. But he left Saudi Arabia roughly a year ago over fears for his safety after writing articles critical of the government, particularly Crown Prince Mohammed bin Salman.
His tweet comes as Saudi Arabia has agreed to allow Turkish investigators to search the Saudi Consulate in Istanbul on Monday, 13 days after Khashoggi, a Saudi journalist, vanished upon entering the mission, three Turkish officials said.More news: Judge rejects Daniels defamation suit against Trump
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Saudi Arabia had earlier denied killing Khashoggi and denounced such assertions as "lies", saying he left the building shortly after entering. "And it sounds like he and also the crown prince had no knowledge", he said, referring to Saudi Crown Prince Mohammad bin Salman.
He said Bangladesh is following the news of the disappearance.
Khashoggi, a Saudi journalist and columnist for the Washington Post newspaper, has gone missing since he entered the Saudi consulate in Istanbul on October 2. Riyadh had so far not allowed the search at the Istanbul consulate - officially Saudi territory - amid reports both sides were at odds over the conditions of the probe.
Khashoggi, who writes for the Washington Post's global opinion section, came to be known as a sharp critic of the Saudi Arabian government.
Late Monday, Khashoggi's family issued a statement in which they acknowledged for the first time that the journalist was no longer alive. "Bangladesh welcomes Saudi Arabia's proposal to form a joint working group with Turkey to investigate the incident".
In Istanbul, meanwhile, Turkish and Saudi investigators began conducting a joint inspection of the consulate. Saudi Arabia is leading a coalition of Gulf states in a military campaign against Iranian-backed Houthi rebels in Yemen.
Khashoggi's fiancée, Hatice Cengiz, who was waiting outside the consulate, says she did not see him re-emerge.
Pompeo was dispatched to Saudi Arabia by Trump, who warned of "severe punishment" for the kingdom if it was involved in Khashoggi's disappearance.