The Saudi ambassador to Washington, Prince Khalid bin Salman, denies the claims the royal family has anything to do with Khashoggi's disappearance.
Turkish officials fear Mr Khashoggi was killed by the Saudis after walking into the kingdom's consulate in Istanbul on October 2, though they have not offered any evidence to support that.
Khashoggi, a Washington Post contributor who had been published in the Arab and Western media, vanished last Tuesday after visiting the consulate to obtain official documents. "He went in and it doesn't look like he came out". Previously Saudi Crown Prince Mohammed bin Salman told Bloomberg that Riyadh would be ready to welcome Turkish officials to search the premises.
A Turkish police source told the Middle East Eye that officials believe Khashoggi was "brutally tortured, killed and cut into pieces" while inside the consulate.
The Saudi consulate has said CCTV cameras were not working that day and has dismissed the murder claims as "baseless".
He said then that Saudi Arabia is before "serious transformation that is going to involve and affect every Saudi".
"Is it possible for there to be no camera systems at the Saudi Arabia consulate, where the event took place?", Erdogan was quoted as saying by Hurriyet.
Khashoggi's fiancé told the authorities that he was required to submit his cell phone to Saudi officials upon entering the building - a practice that is not uncommon.
"Mere words are not enough evidence" to dispute the allegations that Khashoggi had been killed, Erdogan said on Monday. 'We have to find out what happened. Afterward, his body was dismembered to hide the killing, they said the probe found.
Turkish authorities suspect Khashoggi was murdered while inside the building, and President Recep Tayyip Erdoğan says he is now personally involved in the case. the BBC reported.
Pressure, meanwhile, mounted in Congress for the Trump administration to address the writer's disappearance.
In this February 1, 2015, file photo, Saudi journalist Jamal Khashoggi speaks during a press conference in Manama, Bahrain. "We're working with Turkey, and frankly we're working with Saudi Arabia", the USA president said in an interview on the Fox News.
Hatice Cengiz made the appeal in an opinion piece for The Washington Post newspaper, where Khashoggi was a columnist and an outspoken critic of some of Riyadh's policies.
The Post, citing anonymous U.S. officials familiar with the intelligence, said Saudi Crown Prince Mohammed bin Salman ordered an operation to lure Mr Khashoggi from his home in Virginia, where he lived most recently, to Saudi Arabia and then detain him.
The president also reiterated his opposition to punishing Saudi Arabia by blocking arms sales, which he noted are worth $110 billion to the United States.
"And we're being very tough and we have investigators over there and we're working with Turkey and frankly we're working with Saudi Arabia", Trump said in an interview with "Fox and Friends".