During the visit, he met high-ranking Turkish officials and inspected the Saudi consulate premises.
Sharon Squassoni, a research professor at George Washington University's Elliott School of International Affairs, called the letter a "pretty minor request" given the seriousness of the allegations surrounding the death of the Khashoggi, a 59-year-old columnist for The Washington Post. It said it has arrested 18 suspects, who will be prosecuted in Saudi Arabia.
Saudi prosecutor Mojeb held talks with Istanbul's chief prosecutor, Irfan Fidan, at Istanbul's main court house for a second time on Tuesday before heading for the consulate where Khashoggi was killed, Turkish broadcaster NTV reported.
It came in the backdrop of mounting pressure on Saudi to account for the whereabouts of Jamal Khashoggi.
Turkey's relations with Saudi Arabia were strained past year when Ankara sent troops to the Gulf state of Qatar in a show of support after its Gulf neighbours, including Saudi Arabia, imposed an embargo on Doha.
Mohammed bin Salman previously vowed that Khashoggi's killers - which the country has claimed were rogues - would face justice.
No body has been found, and Turkish officials have repeatedly demanded that Saudi officials reveal the location of his remains and identify the "local collaborator" who Saudi officials have said handled the disposal.
United Nations High Commissioner for Human Rights, Michelle Bachelet, has called for worldwide experts to be involved in an independent investigation into the murder of prominent Saudi dissident journalist Jamal Khashoggi, who went missing after visiting the kingdom's consulate in Turkey's largest city of Istanbul earlier this month.
It said Mr Mojeb's response also distanced Riyadh from the idea that a "local cooperator" had been involved, saying that Saudi authorities had not made an official statement to that effect.
Private DHA news agency said Wednesday the prosecutor, Saud al-Mojeb, paid a midnight visit to the Turkish intelligence agency's Istanbul headquarters.
Erdogan's government has pressed Riyadh to conclude its investigation as soon as possible. "The truth has not been revealed", foreign minister Jean-Yves Le Drian told RTL. "No need to prevaricate, it makes no sense to try to save certain people", said Erdogan, who has stopped short of directly blaming the Saudi government.