It was unclear whether Prince Mohammed will accompany him for the remainder of the tour, which comes as Saudi Arabia faces global outrage over Khashoggi's murder on October 2 in its consulate in Istanbul.
"But most concerning is the murder of Jamal Khashoggi", he said, urging Saudi Arabia to "ensure comprehensive and transparent investigations into the murder" and to make sure "those responsible are held to account, and that measures are put in place to prevent any possibility of recurrence".
The so-called Universal Periodic Review - which all 193 United Nations countries must undergo approximately every four years - came as a Turkish official charged Monday that Saudi Arabia had sent experts to Turkey to cover up the journalist's murder before allowing Turkish police in to search the consulate.
A Turkish official, speaking anonymously, confirmed a Monday report in Sabah, a newspaper close to Turkey's government, that chemicals expert Ahmad Abdulaziz al-Janobi and toxicology expert Khaled Yahya al-Zahrani were part of a team sent from Saudi Arabia, supposedly to investigate Khashoggi's October 2 killing.
Turkey has said that a hit squad sent from Saudi Arabia strangled Khashoggi shortly after he entered the consulate to seek a document he needed for his upcoming marriage to his Turkish fiancee.
Turki Bin Abdul Aziz Al-Jasser is said to have been murdered in jail a month after Jamal Khashoggi was slaughtered in the kingdom's Istanbul consulate.
On Friday, Yasin Aktay, an adviser to Turkey's President Recep Tayyip Erdogan and reportedly a friend of Khashoggi's, told the newspaper Hurriyet that the journalist's body had been dissolved after the murder.
Khashoggi's body was 'dissolved' after murder: Erdogan adviser
The source said the body was handed over to a local "collaborator" after the killing, adding that it is not at the Saudi consulate in Istanbul.
Saudi officials provided conflicting explanations for his death before finally admitting he was killed after getting into a brawl with a Saudi security team that had meant to return him to the kingdom.
"All what we want right now is to bury him in Al-Baqi (cemetery) in Medina with the rest of his family", Salah Khashoggi said.
"I really hope that whatever happened wasn't painful for him, or it was quick", he added. Turkish authorities said the team dismembered Khashoggi's body and disposed of it.
Son - whose company has heavily invested in real estate companies like WeWork, Katerra and Lemonade -condemned the attack, but said his company has a "responsibility" to continue to invest the Saudis' funds.
The two individuals carried out clean-up operations at the consulate and the consul's residence in Istanbul until October 17 and left the country three days later, he said. He said he planned to return to his banking job in Jeddah soon and has faith that King Salman's promise that "everybody involved will be brought to justice".
Saudi Arabia acknowledged last month that Turkish evidence indicates that the Khashoggi's killing at the consulate was premeditated, shifting its explanation in an apparent effort to ease worldwide outrage over the death.
He gave no details on the status or whereabouts of the 18 Saudi nationals detained in connection with the case and repeatedly declined to answer journalists' questions about them, saying: "The case is still under investigation, as you know.I think my statement was very clear".