"Turkey will reveal whatever had happened. Nobody should ever doubt about it," said Omer Celik, spokesman for the ruling Justice and Development Party (AKP), the Anadolu news agency reported.
Khashoggi, a Washington Post contributor and critic of the Islamic petro-state's powerful crown prince, was last seen on October 2 entering his country's consulate in Istanbul.
Riyadh's admission came after persistent claims by the Saudi authorities that the journalist had left the consulate alive.
Turkish police and prosecutors this week searched both the consulate as well as the consul's residence in Istanbul.
Celik said it was Turkey's "debt of honour" to reveal what happened.
"We are not accusing anyone in advance but we don't accept anything to remain covered (up)," he said.
Turkish President Recep Tayyip Erdogan on Friday night spoke with Saudi King Salman and the two agreed to continue cooperation in the probe.
In public, Erdogan and top government figures have remained extremely cautious, often referring to a prosecutors' investigation and stopping short of pinning the blame on Saudi Arabia.
Staff members of the Saudi Arabian consulate in Istanbul testified to prosecutors Friday as part of the probe.