Erdogan said earlier on Sunday that he will make a statement and address the issues "in detail" on the Khashoggi case on Tuesday during his party's group meeting at Parliament.
The Istanbul governor's office has put Cengiz, a Turkish national, under 24-hour police protection, Anadolu said. "The incident will be revealed entirely".
Saudi officials maintain that Saudi Crown Prince Mohammad Bin Salman knew nothing of the killing.
The comments from Foreign Minister Adel al-Jubeir were some of the most direct yet from Riyadh, which has given multiple and conflicting accounts about Khashoggi's killing on October 2, first denying his death and later admitting it amid an global outcry.
"The individuals who did this, did this outside the scope of their authority".
"I would cut off arms sales".
"It's my thinking that MBS was involved in this, that he directed this and that this person was purposefully murdered", Sen. "Yes, I think he did it", Senator Bob Corker, chairman of the Senate Foreign Relations Committee, said in an interview with CNN's "State of the Union".
Jubeir called the killing of Khashoggi a awful mistake and offered condolences to his family.
During an appearance Sunday on NBC's "Meet the Press", Sen.
He said he would "love" it if the Crown Prince was not responsible for the murder. "Then Prince Mohammed contacted Khashoggi by phone and tried to convince him to return to Riyadh", the report alleges.
"Even the senior leadership of our intelligence service was not aware of this", Jubeir said.
The Saudi official presented what he said were Saudi internal intelligence documents which appeared to show the initiative to bring back dissidents as well as the specific one involving Mr Khashoggi.
Sen. Rand Paul told "Fox News Sunday" that the US "cannot continue to have relations with him and so I think he's going to have to be replaced".
"We can feel their pain and we wish this didn't happen and I wish that this could have been avoided", he said. "And what happened subsequent to that".
Last Friday, Saudi Arabia admitted that Mr Khashoggi did in fact die in the consulate, but claimed it had occurred during a brawl.
Reuters on Sunday quoted an unnamed Saudi official who portrayed Khashoggi's death as the result of a botched kidnapping.
"Corker is also calling on Turkey, which has said it has tapes from Khashoggi's killing inside the Saudi Consulate in Istanbul, to turn them over to the United States".
Khashoggi's body, the official added, was rolled up in a carpet and given to a "local cooperator" for disposal.
Saudi Arabia faced a growing chorus of incredulity on Sunday, with world powers demanding answers. The team that approached Khashoggi had been sent to negotiate, but "it went south", the official said, adding that "there was no order for a kidnapping".