Trump, speaking to reporters at the White House, said the United States was expecting a report soon on journalist Jamal Khashoggi, but gave no other details.
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Trump also spoke about the disappearance while being interviewed on the Fox & Friends program on Thursday, saying the U.S. is being "very tough" as it looks into the case.
"Well, we're looking at it very, very seriously," Trump said. "I don't like it at all. Now, you don't have American citizens, but that in this case, [it] doesn't matter. I don't like it. I don't like it with respect to reporters. It is a terrible, terrible precedent. We can't let it happen.
"I have to find out what happened … and we're probably getting closer than you might think," he said in the Fox News interview.
Trump also expressed reservations over calls to withhold further U.S. arms sales to Saudi Arabia, saying such a move "would be hurting us."
Video: Raw Politics: What has happened to Jamal Khashoggi?
Thursday evening, The Washington Post, citing unidentified U.S. and Turkish officials, reported that Turkey had told U.S. officials it has audio and video recordings that prove Khashoggi was killed inside the consulate. It was not clear that U.S. officials had seen the footage or heard the audio, the Post reported, but Turkish officials have described the recordings to them.
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Global pressure has mounted on close U.S. ally Saudi Arabia over the whereabouts of Khashoggi, a prominent critic of Saudi policies who entered the consulate on Oct. 2 to get documents for his planned marriage. His Turkish fiancée, Hatice Cengiz, who was waiting outside, said he never reappeared.
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A Turkish police officer stands outside the residence of the Saudi Consulate in Istanbul on Thursday. (Erdem Sahin/EPA-EFE)Turkish sources have previously said they believe Khashoggi was killed inside the building and his body was removed, allegations that Riyadh dismisses as baseless.
The two leaders, each the head of a major regional power, have until now kept their relations cordial in the interest of stability. But during the past week, tensions between them have erupted over the disappearance of Jamal Khashoggi, a Saudi dissident and Washington Post columnist who vanished after entering the Saudi Consulate in Istanbul nine days ago.
A team of investigators is preparing to go into the consulate, where Khashoggi was last seen entering nine days ago, a Turkish security official told Reuters.
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"Now, they are waiting the final permission to enter the consulate," the official said, following an initial offer from Saudi authorities. It was unclear when that might happen.
In the interview, Trump said the United States was working with Turkey and Saudi Arabia, adding, "We have investigators over there."
One U.S. official said there was no intelligence that showed the Saudis wanted to lure Khashoggi to the consulate in Istanbul. Intelligence officials and experts have speculated in recent days that the 15-man Saudi security team that Turkish officials say was sent to Istanbul may have intended to capture Khashoggi and bring him back to Saudi Arabia, and not to kill him.
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But three U.S. law enforcement sources said that because Khashoggi is not an American citizen and disappeared outside the country, the FBI has no automatic jurisdiction to get involved in the case and could only become involved if requested by a foreign government such as Turkey.
Trump told reporters a day earlier that he had raised Khashoggi's case with Saudi Arabia "at the highest level" and more than once in recent days, and said he and his wife expect to invite Cengiz to the White House soon.
Asked about the invitation, Cengiz told Turkish state broadcaster TRT on Thursday: "I am not thinking anything on this subject at the moment."
In an op-ed in the Washington Post on Tuesday, she implored the president and his wife to "help shed light on Jamal's disappearance."
“What has reportedly happened in Turkey around the disappearance of journalist Jamal Khashoggi, if proved true, would clearly change the ability of any of us in the West to do business with the Saudi government,” Branson said in a statement.
Trump made Saudi Arabia the first stop on his first foreign trip as president in May 2017, but in recent weeks has appeared to sour a bit on Riyadh, complaining directly to King Salman about the cost of American support for the Saudi military and for OPEC oil price increases.
Turkish President Tayyip Erdogan said his country was worried about Khashoggi's disappearance and cannot remain silent, in comments quoted by Hurriyet newspaper on Thursday.
"We are investigating all aspects of the event. It is not possible for us to remain silent regarding such an occurrence, because it is not a common occurrence," he said.
He also questioned assertions by Saudi authorities that the consulate does not have footage of Khashoggi leaving the building as the mission's security cameras only provide live footage and do not record images.
"Is it possible for there to be no camera systems at the Saudi Arabia consulate, where the event took place?," Erdogan said.
Pro-government Turkish daily Sabah on Wednesday published preliminary evidence from investigators it said identified a 15-member Saudi intelligence team involved in Khashoggi's disappearance.
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One is a forensic expert who has worked at the Saudi Interior Ministry for 20 years, according to a LinkedIn profile. Other names and photos match officers in the Saudi Army and Air Force, as identified by previous Saudi media reports and in one case a Facebook profile.
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The Saudi Consulate referred Reuters to authorities in Riyadh who have not responded to questions about the 15 Saudis, who Sabah said travelled on diplomatic passports, arriving in Istanbul hours before Khashoggi disappeared.
Turkish police have released images of a black van taken from laneway cameras as part of the search for Jamal Khashoggi:
Khashoggi's disappearance is likely to further deepen divisions between Turkey and Saudi Arabia. Relations were already strained after Turkey sent troops to the Gulf state of Qatar last year in a show of support after its Gulf neighbours, including Saudi Arabia, imposed an embargo on Doha.
If Saudi Arabia is not telling the truth about Khashoggi, he told reporters, why would we believe them that they are not intentionally hitting civilians inside Yemen? Murphy was among seven senators who wrote to Secretary of State Mike Pompeo on Wednesday raising concerns over last months certification that a Saudi-led coalition was taking actions to protect civilians despite what the lawmakers described as a dramatic increase in deaths.
The incident has been largely absent from Saudi media, but on Thursday Saudi-owned newspaper Asharq al Awsat cited an unnamed source who said the kingdom was being targeted by "those who try to exploit the reality of the disappearance."
In Istanbul, Turkish media said that Saudi royal guards, intelligence officers, soldiers and an autopsy expert had been part of the team flown in and targeting Khashoggi. Those reported details, along with comments from Turkish President Recep Tayyip Erdogan, appeared aimed at gradually pressuring Saudi Arabia to reveal what happened while also balancing a need to maintain Saudi investments in Turkey and relations on other issues.
Erdogan, whose AK Party is rooted in political Islam, also supported a government in Egypt led by the Muslim Brotherhood, which Saudi Arabia has designated a terrorist movement.
Earlier this year, Khashoggi told CBC's The National there is "no room for critical dissent" in Saudi Arabia.
Trump maintained that the U.S. is being very tough as it looks into the case of Jamal Khashoggi, a critic of the Saudi leadership and a contributor to The Washington Post who has been missing since Oct. 2. He had entered a Saudi consulate in the Turkish city of Istanbul to get marriage paperwork as his fiancee waited outside and hasnt been seen since.
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