Yamal Aktay said the slain journalist’s body was dismembered to “dissolve his remains more easily”.
The aide to President Erdogan told Hurriyet Daily newspaper: “The reason they dismembered Khashoggi’s body was to dissolve his remains more easily.
“Now we see that they did not only dismember his body but also vaporised it.”
He added: “The murder of an innocent person is one crime. The treatment of the body is a separate crime.”
Last month, 18 men were arrested in Saudi Arabia for their suspected involvement in what Mr Erdogan called the “gruesome murder” of Mr Khashoggi, adding they should stand trial in Turkey.
He said: “This is my proposal and my request because this is where the incident took place.”
Meanwhile the Washington Post said an anonymous official told the publication “biological evidence” found in the consulate’s garden where the writer’s body parts were found suggested that because of acid “Khashoggi’s body was not in need of burying.”
Mr Khashoggi, 57, vanished on October 2 after entering the Saudi Arabia Consulate, sparking a man hunt.
Parts of his body, including his face, were found in in the Saudi Consul general’s garden located 500 metres away from the consulate building in Turkey.
His “disfigured” face was recovered among the shrubbery as well as other body parts, leading Turkish investigators to believe he was “cut up” in the disturbing killing.
The murder sparked calls from President Erdogan that those responsible “be brought to account”, adding Turkey’s investigation into the death would not take place until all questions had been answered.
Saudi Arabia’s Crown Prince Mohammed bin Salman, who has been blamed for the crime, said the murder was “heinous and cannot be justified” after appearing on television two days after body parts were found.
Mr Khashoggi was a Washington Post contributor and critic of the Saudi regime.
His death has brought waves of scrutiny on Saudi Arabia and the Crown Prince, who Mr Khashoggi has personally criticised in the past.