"The victim's body was dismembered and destroyed following his death by suffocation, in line with advance plans", added the statement.
They said the Saudi dissident had been "cut up" and his face "disfigured". Trump told reporters at the White House on Wednesday: "I just hope it all works out".
Saudi Arabia has so far denied the extradition of 18 suspects detained in Riyadh, but officials insist the kingdom will bring them to justice once the investigation is complete.
On Monday, Al-Muajab had an extensive meeting with Turkey's Chief Public Prosecutor Irfan Fidan at the Istanbul Caglayan courthouse.
France said Wednesday that "not enough" was being done to find those responsible for the murder of Khashoggi, who was an insider in Saudi royal circles before going into self-imposed exile in the United States a year ago.More news: Golden Tate Traded To Eagles
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Riyadh has said that the journalist was murdered in the building in what was a rogue operation, and Saudi authorities have arrested 18 individuals in connection with his death.
On 7 October The Washington Post cited a United States official saying Khashoggi's body "was likely dismembered, removed in boxes and flown out of the country". Khashoggi was murdered by Saudi officials, who claim the writer died as a result of an "altercation".
The next day, a source close to the Turkish government says police believe the journalist was murdered inside the consulate "by a team especially sent to Istanbul and who left the same day".
"It's an terrible thing that took place", Pompeo told conservative talk show host Brian Kilmeade. His Turkish fiancee was waiting for him outside.
Khashoggi - a fierce critic of Riyadh's human rights violations and of Crown Prince Mohammed bin Salman's policies - disappeared after entering the kingdom's consulate in Istanbul on October 2 for the paperwork needed for his planned marriage.
Saudi Arabia's attorney general admitted Thursday that evidence shared by Turkish officials suggests that Khashoggi's killing was "premeditated". It recently acknowledged that Turkish evidence shows the killing was premeditated.
Khashoggi, known for his criticism of Saudi policies, had been working as a columnist for The Washington Post.