The Washington Post contributor, 59, vanished after an appointment with Saudi officials on Tuesday.
A source described by Reuters as a "Turkish official" told the wire service, "The initial assessment of the Turkish police is that Mr. Khashoggi has been killed at the consulate of Saudi Arabia in Istanbul".
Turkish police investigating the case said October 6 that 15 Saudis, including several officials, arrived in Istanbul on two planes and entered the consulate while Khashoggi was inside.
'The official strongly denounced these baseless allegations, ' the agency wrote. A US official said that Turkish investigators believe Khashoggi was likely dismembered and his body removed in boxes and flown out of the country.
The ambassador, Prince Khalid bin Salman, reiterated a statement made by other Saudi officials that video cameras at the consulate had not been recording on the day of Khashoggi's visit.
Saudi officials reject the accusations and say that Khashoggi left the consulate premises.
He said The Post was committed to discovering the truth and that if the investigation showed any Saudi government involvement, the news organisation would view it as a flagrant attack on one of its journalists. "As the president of the Turkish Republic I am following it, chasing it and, whatever conclusions come from here, we will inform the world about it", he said. In his speech to the UN General Assembly, the U.S. president in a similar vein cautioned other unnamed countries against taking advantage of the United States.
Erdogan said that he hoped to have the results "very quickly" over the incident involving a "journalist I knew for a long time" and a "friend".
Fred Hiatt, the director of the Washington Post's editorial page, said if the reports were true "it is a monstrous and unfathomable act".
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Khashoggi fled the country in September 2017, months after Prince Mohammed was appointed heir to the throne, amid a campaign that saw dozens of dissidents arrested including intellectuals and Islamic preachers.
A Saudi delegation had arrived in Istanbul to assist with the investigation, the statement said. He writes out of a sense of love for his country and deep faith in human dignity and freedom'.
Turan Kislakci, the head of Turkish-Arab Media Association and a friend of Khashoggi told the New York Times that he spoke to Turkish officials about the case.
That would bring the PIF's contribution to the two funds to US$90 billion, he said.
The official quoted by SPA underlined that Saudi Arabia was responsible for the safety and well-being of all its citizens, wherever they may be, and that its authorities "are diligently following up on this matter to uncover the complete facts".
Asked why his reaction to Canada differed, the crown prince said the Canadians sought to impose their will on Saudi Arabia and infringe on its sovereignty.
The ultra-conservative kingdom in June lifted a ban on women driving.
But since the emergence of Prince Mohammed, 33, as the center of power in the kingdom a year ago, Khashoggi has been openly critical of the monarchy.