Saudi Arabia has admitted that the journalist died in a fight at the consulate on October 2, after having denied any knowledge of his whereabouts for two weeks. It said 18 people had been arrested.
"Turkey will uncover whatever happened. No one should have doubts about that," Omer Celik said in a statement, as quoted by the Anadolu news agency.
Turkish President Recep Tayyip Erdogan is determined to solve the case by all means, the spokesman added. He said Ankara would not blame anyone until the end of the investigation.
Turkish police sources told the agency that 15 Saudis, including officials, travelled to Istanbul on the day Khashoggi disappeared. All of them have since left the country.