Bandar bin Mohammed al-Aiban made the comments as Turkey's Justice Ministry said Interpol had issued red notices - asking police worldwide to locate and provisionally arrest a person pending extradition - for 20 people regarding Mr. Khashoggi's death.
The public prosecutor is seeking the death penalty for five of them.
Bandar bin Mohammed Al-Aiban replied simply that the case was "in the courts" in Saudi Arabia when asked by a reporter to respond to calls that the kingdom accept worldwide support in investigating the killing.
Saudi Arabia has refused to allow any global investigators to look into the murder of journalist Jamal Khashoggi, saying those responsible are already facing justice.
He insisted that his country was "horrified by what has happened pursuant to this unfortunate accident".
Khashoggi, a Washington Post contributor and critic of Crown Prince Mohammed bin Salman, was murdered at the Saudi consulate in Istanbul on October 2.
Meanwhile, human rights groups, as well as dozens of foreign governments, have urged Saudi Arabia to cooperate with a United Nations-led investigation into the crime.
Aiban said the case against the suspects is ongoing and so far, they have appeared in court for three hearings with their lawyers present. Turkey said Saudi authorities should disclose the names of defendants and the charges they face if it wanted to avoid questions over the "sincerity of judicial proceedings in the kingdom".
The Trump administration imposed sanctions on 17 individuals in November, but these did not include several high-ranking Saudi officials implicated in the murder, including the Crown Prince.
"Turkey will continue to serve the cause of justice until Jamal Khashoggi's body is found, the local collaborator (s) are identified, and those who ordered the hit are revealed", Altun concluded, once again emphasizing that the incident must be investigated "to the last detail" and "without being politicized".
This week, more than 30 countries, including all 28 European Union member states, censured the Saudi government at the UN Human Rights Council for its human rights record.