The consulate has other entrances and exits as well, and Saudi officials insist he left through one of them.
In an interview with USA 60 Minutes, Mr Trump said the Saudis denied involvement "in every way you can imagine" when the crown prince spoke to his son-in-law Jared Kushner.
The Washington Post reported on Tuesday that before Khashoggi disappeared, USA intelligence had intercepted communications in which the Saudis had been discussing a plot to abduct him. Reporters Without Borders (RSF), which ranks the kingdom 169th out of 180 on its World Press Freedom Index, said in a statement that between 25 and 30 professional and non-professional journalists are now detained in Saudi Arabia.
'They're in touch and she'll be most likely coming to the White House and we'll work on it together, ' the president said.
Britain's main opposition Labour Party would stop selling arms to Saudi Arabia if it was in government, its foreign policy spokeswoman said on Sunday after the disappearance of Saudi journalist Jamal Khashoggi.
His comments came after the fiancé of Khashoggi, a Washington Post contributor who often criticized the regime of Crown Prince Mohammed bin Salman, urged him to shed light on the matter.
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Broadcast by Turkey's TRT World channel and apparently obtained from security cameras, the footage shows vehicles driving up to the consulate, including black vans thought to be central to inquiries.
Cengiz described how hard it was, in the middle of dealing with Khashoggi's disappearance, to have to cancel all their wedding preparations. "Right now, nobody knows anything about it", he said.
With the mystery over Khashoggi unresolved after he failed to reappear after walking into the consulate on October 2, a pro-government Turkish daily said the Saudi national had recorded his own interrogation inside the mission on an Apple Watch. "We have nothing to hide", he said in an interview with English-language Bloomberg news network.
Sen. Chris Murphy, D-Conn., endorsed a break in the U.S. -Saudi relationship in a tweet last week.
Trump said Tuesday that he hadn't spoken to the Saudis about Khashoggi, "but I will be at some point", according to the Associated Press. "It is not possible for us to remain silent regarding such an occurrence, because it is not a common occurrence", he said. Khashoggi had written columns critical of the Saudi government in The Post in the past year.
Turan Kislakci, a friend of Khashoggi and the head of the Turkish-Arab Media Association, said that Turkish officials said the journalist has been brutally murdered. Jamal's well-being, as a Saudi citizen, is our utmost most concern and we are focusing on the investigation as a means to reveal the truth behind his disappearance.
The Washington Post also reported on Tuesday that USA intelligence officials had intercepted communications of Saudi officials discussing a plan to kidnap Khashoggi. The Turkish leader rejected commenting on allegations that Khashoggi was killed at the consulate, but said he was anxious, Efe news reported.