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 Khashoggi's death.
Despite claims Qahtani was sacked by the Saudi leadership in the aftermath of Khashoggi's murder, the Washington Post and Wall Street Journal have reported that Qahtani continues to advise the crown prince.
The head of a Saudi delegation speaking before the UN Human Rights Council in Geneva insisted that his country was taking all the "measures required for us to resolve this heinous crime".
He said his country "refutes completely" calls for parts of the legal process to be "internationalized", saying such demands cast doubt on the integrity of the Saudi judicial system.
We deeply regret that Saudi Arabia rejected a recommendation to fully cooperate with United Nations human rights mechanisms to investigate allegations of violations of worldwide humanitarian law in Yemen.
The Turkish Justice Ministry said it had requested Interpol red notices for 18 people on November 15 and for two more on December 21 without identifying the individuals.
Interpol issued the notices on March 1, the ministry said on Twitter, without giving further details on the suspects.
It also criticized Aiban's rejection of any foreign investigation.
The Saudi government has denied any involvement by the crown prince.
The Saudi public prosecutor's spokesman said late previous year that 11 Saudis had been indicted and referred for trial over the case, with authorities seeking the death penalty for five. Although Saudi prosecutors are seeking the death penalty over the incident, he assured that those found guilty were not being tortured.