Otaibi left Istanbul on Tuesday for Riyadh ahead of a planned search of his residence as part of the official Turkish investigation into Khashoggi's disappearance.
Pressure is growing on Saudi Arabia to give a full explanation of what happened to him.
"What we have right now is Mike Pompeo, who's terrific, who's doing a great job, Secretary of State, is with the King right now and the Crown Prince literally as we speak and we're trying to find out what went on", Trump answered.
The Saudis have strongly denied those allegations, but U.S. media outlets have reported they will acknowledge he was killed in a botched interrogation.
Until Monday, Riyadh had not allowed Turkish investigators to search the consulate, with reports both sides were at odds over the conditions.
What has come out of the Pompeo meeting?
"Well this is not rogue killers, this is a rogue crown prince", Graham said in a separate interview with Fox News Radio. On Monday he echoed Saudi talking points after a brief phone call with the Saudi king.More news: QUIZ: How well do you know basic pot rules across Canada?
Mr Pompeo is expected in Turkey later.
Iran, as the regional rival to Saudi Arabia, would be the prime beneficiary if the Saudis were to lose their defensive U.S. umbrella.
"In view of the seriousness of the situation surrounding the disappearance of Khashoggi, I believe the inviolability or immunity of the relevant premises and officials bestowed by treaties such as the 1963 Vienna Convention on Consular Relations should be waived immediately", Ms Bachelet said.
Though the Khashoggi case has dominated his talks so far, Pompeo has raised other issues on his last-minute trip.
What are United States media reporting?
The Daily Beast reported that Saudi officials plan to pin Khashoggi's death on an unnamed Saudi two-star general, citing two anonymous sources familiar with the matter.
The intention had been only to abduct him from Turkey, the sources said.
"They made a commitment, too, to hold anyone connected to any wrongdoing that may be found accountable for that whether they are a senior officer or official", Pompeo said.
Cavusoglu once more asserted that Saudi Arabia must cooperate with Turkey in all matters regarding the missing journalist probe.More news: Zainab's murderer hanged at the Kot Lakhpat Jail
What happened with the consulate search?She and Turkish authorities say he never emerged and he has not been heard from since.
Just hours before the forensic inspection, the Saudis let in a team of cleaners armed with several large mops and buckets.
They reportedly took with them samples, including of soil from the consulate garden and a metal gate.
Mr Erdogan said: "The investigation is looking into many things such as toxic materials and those materials being removed by painting them over".
What allegedly happened in Istanbul?
According to Turkish police, al-Tubaigy was one of the 15 Saudis who had arrived in Istanbul on two planes and entered the consulate while Khashoggi was inside.
The president suggested on Monday that Khashoggi could have been murdered by "rogue killers".
"It has been 13 days since the event, so surely proving some of the evidence might be difficult" the Turkish official said.
Officially entitled the Future Finance Initiative, the Saudi conference describes itself as an "international platform for expert-led debate between investors, innovators and governments as well as economic leaders". He is a United States resident.More news: KPRC2 Fans look ahead to Game 4 of ALCS