The President said the King denied any knowledge of what had happened to Mr. Khashoggi, a columnist for The Washington Post who had been critical of the Crown Prince. However, in a contrary scenario, the kingdom, highly criticized due for the actions of Crown Prince Mohammed bin Salman, will remain as a rogue state in the global system.
President Donald Trump on Monday talked to the Saudi King, during which the latter flatly denied having any knowledge of the missing journalist.
Pompeo will head to Turkey on Wednesday, the BBC said.
Police plan to search the Saudi consul general's home, as well as some of the country's diplomatic vehicles, Turkish Foreign Minister Mevlut Cavusoglu said.
Turkish officials say they fear a Saudi hit team killed Khashoggi, who has been missing almost two weeks.
They are obliged to take all measures to prevent torture, enforced disappearances and other serious human rights violations to investigate allegations of acts constituting these crimes, and to bring to justice those suspected of committing them, she said.
Khashoggi entered the consulate to collect some papers before his forthcoming marriage with his fiancée waiting outside.
He declared in July that he believed Russian President Vladimir Putin's claim that the Russians did not interfere in the 2016 presidential election - siding with Putin over USA intelligence officials, who say they have plentiful evidence that Moscow mounted a calculated effort to help Trump win the election.
Pompeo said the Saudis are committed to a "thorough, transparent and timely" investigation.
Saudi Arabia has denied these reports.
It stated that one of the suspects was a "frequent companion" of Salman who was alongside the crown prince during visits to Paris, Madrid, Houston, Boston, and the United Nations, publishing photos showing the suspect in Salman's entourage.
Saudi journalist Jamal Khashoggi was tortured before being decapitated inside Riyadh's consulate in Istanbul, pro-government daily Yeni Safak reported Wednesday, saying it had heard audio recordings of the incident.
The Turkish security source confirmed that Saudi Consul General Mohammad al-Otaibi left Istanbul on Tuesday, returning to Riyadh, hours before his residence was set to be searched.
Prominent U.S. newspapers 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.
Mr. Trump also said that his former personal lawyer, Michael Cohen, was "lying" when he said under oath that Mr. Trump had directed him to use campaign funds to pay off two women who alleged that they had an affair with Mr. Trump.
"They are trying to make fun of us and our willingness to cooperate", one of the officials said.