The case has brought near unprecedented worldwide scrutiny on Saudi Arabia, which is seeking to draw a line under the crisis after offering a series of differing narratives in the weeks following Khashoggi's murder.
She was speaking at a joint news conference with French President Emmanuel Macron as well as Russian President Vladimir Putin and Turkish President Recep Tayyip Erdogan at the conclusion of a four-way summit on Syria.
Top Saudi and Turkish prosecutors on Monday discussed the investigation into the killing of Saudi writer Jamal Khashoggi, a show of co-operation amid Turkish demands that Saudi Arabia turn over 18 detained suspects for a murder trial.
Turkey is seeking the extradition of the Saudi suspects detained for the killing in the Saudi Consulate, which happened after Khashoggi entered the building on October 2.
Turkey called on Monday for the full truth surrounding the killing of Saudi journalist, Jamal Khashoggi, to be revealed, as Saudi Arabia's public prosecutor holds talks in Istanbul. U.S. Defense Secretary Jim Mattis has said the killing undermines regional stability and has urged Saudi Arabia to conduct a full and complete investigation.
Some of those implicated in the killing are close to Crown Prince Mohammed bin Salman, whose condemnation of the killing has failed to ease suspicions that he was involved.
Cavusoglu called on Riyadh to conclude the investigation as soon as possible.
The Saudi prosecutor traveled to Istanbul after acknowledging last week that the killing was "premeditated", based on the evidence of a Turkish investigation, contradicting a previous official statement that it happened accidentally. Ankara has already requested Riyadh to extradite the 15 suspects, but the request has been denied, with Saudi Foreign Minister Adel al-Jubeir said those behind the killing would be prosecuted in the kingdom.
"Turkey, with the evidence that they have compiled, will ensure that there is more than one review of what is going on here", Mattis said.
Turkey's Anadolu news agency said Mojeb was expected to inspect the Saudi consulate.
Turkey has been pushing Saudi Arabia to help locate Khashoggi's body, which has not been found.
He said: "When I asked him why he was anxious, he didn't really want to reply, but eventually he told me he was getting proof that Saudi Arabia had used chemical weapons".
On Sunday, British Sunday Express weekly, citing "highly-placed" intelligence sources, reported that a "member of the royal circle" of Saudi Arabia had ordered to kidnap the journalist and take him back to the Arab kingdom.