The Post, citing anonymous US officials familiar with the intelligence, said Prince Mohammed ordered an operation to lure Khashoggi from his home in Virginia, where he lived most recently, to Saudi Arabia and then detain him.
Trump said he and his administration are "looking at it very, very seriously".
Jack Dorsey, Twitter CEO, was the main target for those activists, as he is known for having good relations with the Saudi Crown Prince.
Neil Quilliam, a senior research fellow for the Middle East and North Africa at the Chatham House think tank, said the Saudis were sure to notice when Trump said he knew "nothing" about Khashoggi's case.
The State Department said today it's still trying to sort out what happened to a missing Saudi journalist who had been living in exile in America for a year due to his high-profile criticism of the kingdom's rulers.
Turkish officials say they fear Saudi Arabia killed and dismembered Khashoggi, without offering evidence explaining why they believe that.
Khashoggi had entered the consulate to get documents for his forthcoming marriage.
On Monday President Trump said that he was "concerned" about reports on Khashoggi's disappearance. Their ambassador to the U.S. insists that he personally had a friendly relationship with Khashoggi and remained in contact whenever both of them were in Washington.
Cengiz wrote on Tuesday: 'After seeing how relaxed he was, I waited patiently and full of hope. Saudi Arabia may have agreed to the search in order to reassure its Western allies and the global community.
A report Monday in the daily newspaper Sabah said investigators were also focused on a convoy of diplomatic vehicles that departed from the consulate on the day Khashoggi vanished.
Government sources said police believe the journalist was killed inside the consulate.
Saudi Arabia has called the allegations baseless.
"There is a video of the moment of him being killed", Kemal Ozturk, a columnist in a pro-government newspaper and the former head of a semiofficial news agency, said in an interview on a pro-government television network Tuesday, the Times reported.
It says the journalist left the consulate shortly after arriving, while Turkey says he was not seen leaving the building.
There he wrote opinion pieces for the Washington Post and continued to appear on Arab and Western TV channels.
The ambassador said the Istanbul consulate is fully cooperating with local authorities and that a Saudi team was sent to Istanbul to cooperate with their Turkish counterparts.
That means Turkish police can not enter and search the consulate unless they get permission from the Saudi authorities, which they have now reportedly received.
She said Mr Khashoggi was required to surrender his mobile phone, which is standard practice in some diplomatic missions.
Jeremy Hunt has warned Saudi Arabia that "friendships depend on shared values" after questioning the country's ambassador over the disappearance of a journalist.
Accusations the Saudi leadership directly ordered the alleged assassination of Khashoggi will put further pressure on the United States and other allies to demand a transparent investigation, with possible serious repercussions to bilateral relations if it doesn't come to fruition.
He has also criticised Saudi Arabia's role in Yemen, where Riyadh leads a military coalition fighting alongside the government in its war with Iran-backed rebels. "The free world deserves answers".
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