Yamal Aktay said the body of the killed journalist had been dismembered to "easily disperse his remains".
President Erdogan's adviser told the Hurriyet Daily: "The reason they dismembered Khashoggi's body was that it was easier to disperse his remains.
"Now we see that they have not only dismembered his body, but have also evaporated."
He added, "Murder of an innocent person is a crime. The treatment of the body is a separate crime. "
Last month, 18 men were arrested in Saudi Arabia for their alleged involvement in the murder of Mr. Erdogan, known as "cruel murder", by Khashoggi.
He said, "This is my suggestion and my request, because the incident happened here."
In the meantime, the Washington Post said an anonymous official told the publication "Biological Evidence" found in the Consulate's garden, where the body parts of the writer were found.
Mr. Khashoggi, 57, disappeared on October 2 after joining the Saudi Arabian consulate, triggering a manhunt.
Parts of his body, including his face, were found in the garden of the Saudi Consul General 500 meters from the consulate building in Turkey.
His "disfigured" face was recovered between the shrubs and other parts of the body, so that Turkish investigators believed he had been "dissected" in the disturbing murder.
The murder sparked calls for President Erdogan to "hold accountable" those responsible. The addition of Turkey's investigation into death would not take place until all questions had been answered.
Saudi Arabia's Crown Prince Mohammed bin Salman, who was charged with the crime, said the murder was "abhorrent and can not be justified" after he appeared on television two days after locating body parts.
Mr. Khashoggi was a Washington Post contributor and a critic of the Saudi regime.
His death has brought waves to Saudi Arabia and the Crown Prince, whom Mr. Khashoggi personally criticized in the past.