It has been nearly two weeks since Khashoggi was last seen, stepping through the grey metal gates to the Saudi mission at 1.14 pm local time on October 2 to organise paperwork for his wedding.
Turkey says it believes he was killed inside, telling US officials that it has audio and video recordings from his final moments to prove it. Saudi Arabia has vehemently denied having anything to do with the disappearance.
Turkish officials have expressed frustration at the Saudis' level of cooperation, having still not been allowed access to the consulate building, despite promises.
Three days after Khashoggi disappeared, Saudi Arabia's Crown Prince Mohammed bin Salman said in an interview with Bloomberg that Turkish authorities were welcome to search inside the consulate. "We have nothing to hide," he said.
In an interview with Lesley Stahl of CBS' 60 Minutes that is airing today, Trump called the journalist's suspected murder "really terrible and disgusting".
"We would be very upset and angry if that were the case," he said of Saudi Arabia's potential responsibility. "As of this moment, they deny it, and they deny it vehemently. Could it be them? Yes."
Later, at the White House, he reiterated that there would be "powerful consequences" for Saudi Arabia.
The stronger line from the Administration follows the release of American pastor Andrew Brunson, who had been held for two years in Turkey and was the focus of a diplomatic dispute between Ankara and Washington.
- additional reporting Daily Telegraph