Erdogan told reporters that authorities were examining camera footage and airport records as part of their investigation into the disappearance last week of Khashoggi, who had been increasingly critical of Saudi Arabia's rulers.
Saudi Arabia's consul-general in Istanbul gave local staff the day off last Tuesday, when Mr Khashoggi vanished, according to Turkish media.
Saudi dissident Jamal Khashoggi speaks at an event hosted by Middle East Monitor in London, Sept. 29, 2018.
Turkish officials told the The Washington Post and Reuters on Saturday that Khashoggi was killed inside the consulate.
Khashoggi, a U.S. resident, has written articles over the past year critical of Saudi Crown Prince Mohammed bin Salman.
"As if the Saudi authorities were asleep and there was a odd silence at a time when the news of Khashoggi's disappearance was spread in the world", he noted.
"Jamal has many friends in the Kingdom, including myself", Khalid wrote.
Turkish officials say Mr Khashoggi was killed on the premises and his body was then removed.
The disappearance of Khashoggi, previously a prominent newspaper editor in Saudi Arabia and an adviser to its former head of intelligence, has sparked global concern, particularly after Turkish sources said over the weekend that authorities believed he was killed inside the consulate. An investigation revealed that, on Tuesday morning, the day when Khashoggi was scheduled to return to the consulate, 12 Saudi officials arrived in Istanbul in two private jets, and went to the consulate.
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Meanwhile, Turkish President Recep Tayyip Erdogan said "God willing, we will not be faced with the situation we do not desire" when asked by journalists about Khashoggi.
Erdogan said the Saudi consulate should have surveillance cameras and should be able to show the video of Khashoggi leaving the building. She and Turkish officials say he never emerged, even though Saudi Arabia insists he left the building.
Turkey's foreign ministry on Wednesday summoned Saudi Arabia's ambassador over the issue.
"The Kingdom of Saudi Arabia conveys its regards to the brotherly Republic of Turkey", a diplomatic note sent to the Turkish foreign ministry said.
The consulate rejected the claims that the journalist was killed there as "baseless", in a Twitter message.
A Turkish official separately told The Associated Press that authorities believe Jamal Khashoggi was slain at the Saudi Consulate, while another said it was a "high probability". He has lived in the United States since previous year to avoid possible arrest, and has written a series of columns for the Post on Saudi affairs. Turkey, it said, must back up its conclusion Khashoggi was killed by making public any evidence it has.
Khashoggi was right about Saudi repression. Khashoggi's fiancee could not immediately be contacted but she said in a Tweet that there had been no official confirmation of the Turkish sources' statements. "A team of 15 Saudis arrived on two planes to carry out the killing, officials have said", 'The Washington Post' reported.
Fusun Arsava, an global law professor at Ankara's Atilim University, told Al-Monitor that even if reports of Khashoggi's murder were true, that would be extremely hard for the Turkish authorities to prove.