He said the killing of Saudi journalist was planned four weeks ago.
The president has also asked Saudi officials to disclose who ordered the killing of Khashoggi and sent the team to Istanbul.
On Monday, Saudi Arabia's top prosecutor, Saud al-Mojeb, met with Istanbul's chief public prosecutor, Irfan Fidan, for an hour and 15 minutes at Istanbul's main courthouse, Turkey's state-run Anadolu news agency said.
Khashoggi was allegedly killed by Saudi agents at their consulate in Istanbul, Turkey, on October 2.
Michelle Bachelet said she welcomed efforts by Saudi and Turkish authorities to investigate and prosecute the alleged perpetrators.
Turkey has given its first official statement on how writer Jamal Khashoggi was killed, saying he was immediately strangled, then dismembered.
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That ad was part of a blitz by Trump's campaign, and his campaign manager, Brad Parscale, did several interviews to promote it. Trump's presidential re-election campaign paid for the ad, United States news media reported. "I hope this doesn't work".
He also claimed that Mojeb was in pursuit of Khashoggi's phone, which the journalist handed to his Turkish fiancee before entering the consulate.
Turkey has stopped short of blaming Saudi Arabia, but hinted that the murder could not have taken place without orders from someone in a senior position.
According to Turkish officials, Khashoggi was attacked the moment he entered the consulate, his fingers were severed, and he was injected with a drug before being dismembered by an autopsy specialist who arrived in Istanbul with a bone saw, wrote the board.
"Either the Saudi foreign minister or the 18 suspects must explain who the local co-conspirators are", Erdoğan said. Cengiz raised an alarm after Khashoggi failed to re-emerge from the Saudi consulate.
In wake of the murder, Germany suspended export licenses to Saudi, while US Secretary of State Mike Pompeo invalidated visas of Saudi officials who are believed to be part of the plot to murder the journalist.
Saudi Arabia changed its story several times, before admitting he died in the consulate and evidence showed the killing was premeditated.