The UN has repeatedly called on Saudi Arabia to cooperate with an UN-led investigation into Khashoggi's murder, but the kingdom has refused, calling it an internal matter.
He insisted that his country was "horrified by what has happened pursuant to this unfortunate accident".
President of Saudi Arabia's Human Rights Commission (HRC), Dr. Bandar al-Aiban, has said the Kingdom brought perpetrators of Khashoggi murder to justice and they have attended three hearings with their lawyers.
Khashoggi, who worked as a contributor for The Washington Post, was an outspoken critic of Crown Prince Mohammed bin Salman.
The State Department noted that in the past, Saudi Arabia did not punish officials accused of committing human rights abuses. He gave no names or other details, however, as the suspects' identities have not yet been made public.
"What is being conveyed by certain media regarding the need for us to internationalise some of these matters is something we do not accept because such demands amount to interference in our domestic affairs and in our domestic judicial system", he told the forum in Geneva.
The suspects, he said, "were entitled to a fair trial. and none of their human rights have been violated, and they have been subjected to no form of torture or cruel and inhuman treatment". "Such demands made upon us are tantamount to the global community doubting the integrity of our judicial apparatus and doubting the independence of our judiciary", he said.
His presentation came after 36 countries last week issued a joint statement demanding justice following the killing, in an unprecedented rebuke of the oil-rich kingdom at the rights council. In a statement read by Iceland's United Nations ambassador Harald Aspelund, the group said, "Investigations into the killing must be prompt, effective and thorough, independent and impartial, and transparent".
Khashoggi's death sparked worldwide outrage and focused a global spotlight on the crown prince.
Khashoggi was killed in the kingdom's Istanbul Consulate on October 2, 2018, by a team of 15 people consisting of Saudi officials who arrived in Turkey for his murder and a cover-up team also in charge of dismembering Khashoggi's body.
Interpol has issued a red notice for the arrest of 20 suspects believed to be involved in the killing of Saudi journalist Jamal Khashoggi, including a top adviser to Saudi Arabia's powerful crown prince, Mohammed bin Salman. In an interview with Al Jazeera, Assiri said Aiban's refusal to allow an worldwide independent investigation suggests officials at the highest levels "are hiding something".
"They are hiding the name for the person who ordered this operation".