Earlier, U.S. President Donald Trump gave Saudi Arabia the benefit of the doubt in Khashoggi's disappearance, while U.S. lawmakers pointed the finger at the Saudi leadership and Western pressure mounted on Riyadh to provide answers.
Pompeo had just come from Riyadh, where he spoke Tuesday with Saudi King Salman and Crown Prince Mohammed bin Salman.
Earlier, US media reported that the Turkish authorities had identified five suspects in the case of Khashoggi's vanishing, four of whom had ties to the Saudi government, including the crown prince.
President Trump compared allegations that the Saudi government authorized the killing of Washington Post columnist Jamal Khashoggi to accusations of sexual misconduct against Supreme Court Justice Brett Kavanaugh.
The top American diplomat will meet his Turkish counterpart Mevlut Cavusoglu to discuss bilateral and regional issues including Syria, the Turkish foreign ministry said in a statement.
But some lawmakers in the USA have all but accepted Turkey's version of the events, that a team of Saudi agents arrived in Istanbul and killed Khashoggi when he went to the consulate.
The US state department said Prince Mohammed agreed there must be a thorough and transparent investigation into the journalist's disappearance.
Otaibi left Istanbul on Tuesday for Riyadh after police said they planned to search his home as part of their investigation into Khashoggi's disappearance.
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Turkish officials say they fear that Khashoggi, a prominent Saudi journalist who had been in living self-imposed exile in the United States, was killed and dismembered after he entered the consulate.
Turkish police on Monday night undertook an eight-hour search at the consulate, taking away soil and DNA samples, although a search expected on Tuesday at the consul's residence has so far not taken place.
Asked if that would include members of the royal family, he said: "They made no exceptions on who they would hold accountable".
Khashoggi vanished after entering the consulate for official documents ahead of his upcoming wedding to his Turkish fiancee.
Speaking with reporters on the White House lawn, Trump once again emphasized that the Saudi government "firmly denies" that it had anything to do with Khashoggi's disappearance, and he suggested that there was another culprit to blame.
Trump has previously threatened "severe punishment" if it turns out Khashoggi was killed in the consulate, though he said Washington would be "punishing" itself if it halted military sales to the country.
USA media reported on Monday that Saudi Arabia would admit that the disappearance and alleged death of Khashoggi was the result of an interrogation gone wrong.
"I think we'll also be guided by what other countries are doing", he said.
France, Germany and Britain on Sunday expressed concerns over the case, calling for "a credible investigation" into the incident.
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