Saudi Arabia's conflicting accounts of Khashoggi's killing have prompted international outcry against the world's top oil exporter, upending the young crown prince's international image as a reformer.
Turkey has released a stream of evidence challenging the initial Saudi denials of involvement, and continues to press Riyadh for details.
On Monday Vice President Fuat Oktay called for an investigation into newspaper reports last week that Khashoggi's body was disposed of by dissolving it in acid.
"The question now is who gave the orders. This is what we are seeking answers to now," Fuat Oktay told Anadolu news agency. "Another question is where the body is... There are reports of (the body) being dissolved with acid now. All of these need to be looked at".
In an article in the Washington Post on Friday, Erdogan said the order to kill Khashoggi came from the "highest levels" of the Saudi government and called for the "puppetmasters" to be unmasked.