After speaking with the king, Trump floated the idea that "rogue killers" may have been responsible for the disappearance. "But we want to find out what happened and he's got instructions to find out what happened".
Khashoggi had penned articles critical of the country's rulers.
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. The members arrived by unmarked police cars but said nothing to journalists waiting outside as they entered the building.
Turkish President Recep Tayyip Erdogan told reporters the investigation "was looking into many things such as toxic materials and those materials being removed by painting them over".
Pompeo met with Saudi Arabian King Salman and the crown prince in Riyadh on Tuesday.
Speaking to journalists in Geneva amid news reports that details of Khashoggi's death may surface soon, indicating that it was an accident, United Nations human rights office (OHCHR) spokesperson Rupert Colville said potentially serious crimes had been committed and the perpetrators should be held accountable. Their search included the roof and garage, and employed a drone to surveil the premises.
Meanwhile, Arabic channel Al-Jazeera quotes Turkey's attorney-general's office as saying it has found evidence to back claims that Mr Khashoggi was killed inside the mission.
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"Yesterday evening, unfortunately, police could not search the Saudi consul's residence".
After his talks in Riyadh on Tuesday, Pompeo was expected in Turkey today to meet Turkish Foreign Minister Mevlut Cavusoglu.
Trump said Pompeo may go to Turkey after Saudi Arabia.
On Sunday, Riyadh angrily rejected political and economic "threats" over the case of the missing journalist and said it would respond to any punitive action "with a bigger one". Following Trump's comments about the possibility that "rogue killers" might have been involved, several U.S. media outlets reported that a Saudi probe was expected to paint Khashoggi's death as a result of a botched rendition and interrogation.
Trump has threatened "severe punishment" if it turns out Khashoggi was killed in the consulate, although he has ruled out cancelling arms deals worth tens of billions of dollars with Saudi Arabia. Another is identified in a diplomatic directory from 2007 as a first secretary at the Saudi Embassy in London.
While Pompeo was in his meetings in Saudi Arabia, Trump, in Washington, said on Twitter, "For the record, I have no financial interests in Saudi Arabia (or Russian Federation, for that matter)".
Reports suggest an assault and struggle took place in the consulate after Mr Khashoggi went to get paperwork for his forthcoming marriage.
"Here we go again with you're guilty until proven innocent", Trump told The Associated Press as he compared the allegations against Saudi Arabia to the sexual misconduct allegations from multiple women against Supreme Court Justice Brett Kavanaugh during his confirmation hearing. "I don't like that".