In Turkey earlier Tuesday, a high-level Turkish official told the AP that police investigators searching the Saudi Consulate had found evidence that Khashoggi was killed there.
Before leaving Riyadh, Pompeo told reporters that Saudi officials pledged they would hold any wrongdoers accountable, no matter how high their positions. Mr. Trump added with a jovial touch.
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".
Turkish sources say cars with diplomatic plates were seen driving between the consulate and the consul's residence on the day Mr Khashoggi was last seen.
Trump called Pompeo on Sunday night and asked him to have face-to-face meetings with the Saudi leaders, State Department spokeswoman Heather Nauert said. Their search included the roof and garage, and employed a drone to surveil the premises.
Mohammed al-Otaibi, the Saudi consul general, apparently left on a 2pm flight as security forces set up barricades outside his residence in the city.
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Overnight, Turkish police completed a search of the consulate after being allowed in by Saudi authorities.
Turkey's state-run Anadolu news agency said Pompeo was expected in Turkey on Wednesday to meet Turkish Foreign Minister Mevlut Cavusoglu, after talks in Riyadh.
The newspaper said one of the Saudi "torturers" replied: "Shut up if you want to live when you return to (Saudi) Arabia". "The Saudi regime has had an appalling human rights record, including inflicting abuses against journalists", Smith pointed out. An investigation is underway about the disappearance and a possible extra-judicial killing of the journalist Khashoggi.
The recording also revealed Mr Khashoggi had fingers cut off and was told to "shut up" or face being killed, Yeni Safak reported.
Trump made the comment after he said Saudi King Salman strongly denied to him any knowledge of what happened. He's going to probably over the next couple of hours - sometime prior to your show, but he will be getting back to me. "I don't like that".
Prince Mohammed, 33, a son of King Salman, consolidated his control in June 2017 when he was named Crown Prince to replace his cousin, Mohammed Nayef, who was sacked.
He had been critical of Prince Mohammed, who has cracked down on dissent with arrests.
Members of the US Congress, including some of Mr Trump's fellow Republicans, are among the loudest voices in the US demanding answers and action on Mr Khashoggi, who moved to Washington previous year fearing retribution for his critical views on the Saudi leadership.
"This guy is a wrecking ball".