Hadid said such a cover-up may have been undertaken to preserve Saudi Arabia's global business ties.
Saudi Arabia said early on Saturday that Khashoggi, a critic of the country's de facto ruler Crown Prince Mohammed bin Salman, had died in a fight inside its consulate in the Turkish city. Saudi TV also confirmed that General Ahmad al-Asiri, deputy director of General Intelligence Directorate, was sacked over the incident. The statement also did not shed any light on what happened to Khashoggi's body after his death.
Late Saturday, the EU's foreign policy chief, Federica Mogherini, called for a "thorough, credible and transparent investigation" into the "deeply troubling" circumstances of Khashoggi's death.
After two weeks of denials, the Saudi Arabian government has admitted Mr Khashoggi died in the consulate, though it has not said what happened to his body.
Saudi Arabia initially denied any knowledge of the disappearance of Khashoggi, who vanished after entering its consulate on October 2.
Saudi Arabia's Gulf ally, the United Arab Emirates, welcomed the moves by the king, as did Egypt.
Trump said he found Saudi Arabia's explanation "credible" and described it as an important first step.
After talks in Copenhagen, Danish Prime Minister Lars Lokke Rasmussen said, "We haven't been told the full truth, and we must insist on getting that", Bloomberg reports.
The decision to overhaul the intelligence apparatus and sack members of the crown prince's inner circle is created to "distance the crown prince from the murder", said analysis firm Eurasia Group.
Turkish media said earlier this week they had identified a 15-member team of suspected Saudi agents who flew into and out of Istanbul on the day of the disappearance.
Mr Trump stressed the importance of Saudi Arabia as a counterbalance to Iran in the Middle East, and pushed back against the need for sanctions against the country in light of the new information, talking about the effect of such a move on the U.S. economy. This has been a awful event.
His disappearance had been shrouded in mystery, with Turkish officials accusing Saudi Arabia of carrying out a state-sponsored killing and dismembering the body.
October 17: Turkish authorities begin searching the consul's residence in Istanbul.
Riyadh also gave Turkey a permission to conduct searches at the residence of the Saudi consul general after the diplomat left Turkey on Tuesday.
U.S. Secretary of State Mike Pompeo discussed the Khashoggi's disappearance during an interview Friday with VOA contributor Greta Van Susteren.
Saudi Arabia said that 18 suspects were in custody and that intelligence officials have been fired. That we don't approve of that kind of activity.
According to the Turkish Sabah newspaper, at least part of the evidence came from an audio recording made from Khashoggi's Apple Watch.
Also Saturday, a senior official in Turkey's ruling party said Ankara would "never allow a cover-up" of Khashoggi's killing.
But amid growing pressure at home and overseas over his soft posture toward Saudi Arabia, Treasury Secretary Steve Mnuchin withdrew from a high-profile investment summit scheduled to begin in Riyadh later this month, and Trump on Thursday seemed to warn that there would be "severe" consequences for Riyadh if it was found responsible for Khashoggi's death.
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