Mr. Khashoggi, a USA resident, Washington Post columnist and leading critic of the powerful Saudi Crown Prince, Mohammed bin Salman, vanished after entering the Saudi consulate in Istanbul nearly two weeks ago to get marriage documents.
Trump wrote: "Just spoke to the King of Saudi Arabia who denies any knowledge of whatever may have happened 'to our Saudi Arabian citizen.' He said that they are working closely with Turkey to find answer". "It sounded to me like maybe these could have been rogue killers".
Khashoggi has written extensively for the Washington Post about Saudi Arabia, criticising its war in Yemen, the recent diplomatic spat with Canada and its arrest of women's rights activists after the lifting of a driving ban for women.
Prince Mohammed, 33, a son of King Salman, consolidated his control in June 2017 when he was named Crown Prince to replace his cousin, Prince Mohammed bin Nayef, who was sacked.
CNN reported Monday, citing sources, that "Saudis are preparing a report that will acknowledge that Saudi journalist Jamal Khashoggi's death was the result of an interrogation that went wrong, one that was meant to lead to his abduction from Turkey".
"The Turkish crime scene investigators carried out searches in the consulate and took the things deemed necessary", a senior Turkish official said, after acknowledging the difficulty of collecting evidence 13 days after the alleged incident. "Trump accepting Saudi Arabia's Khashoggi story without a thorough, independent investigation only enables authoritarian behaviour", said Senator Ed Markey. However, after a telephone conversation with King Salman, US President noted that "rogue killers" could be behind the Washington Post journalist's disappearance and suspected murder.
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Reports suggest an assault and struggle took place in the consulate after Mr Khashoggi went to get paperwork for his forthcoming marriage.
Missing journalist Jamal Khashoggi's Turkish fiancee Hatice Cengiz wait in front of the Saudi Arabian consulate in Istanbul on October 3, 2018. You talk to experts, and this is what they say. European allies have urged "a credible investigation" and accountability for those responsible.
"The Turks have leaked so much that it is inconceivable that they would settle for less than telling the world exactly what happened", said Tamimi, who met Khashoggi for lunch in London the day before he disappeared.
Great Britain, France and Germany also vowed retaliation.
Bahrain's foreign minister called for a boycott of the ride-hailing company Uber Technologies [UBER.UL] after its chief executive officer said he will not attend a business conference in the kingdom's ally Saudi Arabia. Saudi stock index was down 3 percent in early Tuesday trade before it recouped some losses for a decline of 0.5 percent by 0949 GMT. His fiancee, friends and Turkish authorities have said he did not leave the building.
Prince Mohammed has aggressively pitched the kingdom as a destination for foreign investment.
Concern over Khashoggi's disappearance has seen media organisations and a growing number of guests pull out of a "Davos in the Desert" investment conference set for October 23-25, which has become the biggest show for investors to promote Prince Mohammed's reform vision.