The dissident Saudi journalist's Turkish colleagues and several Turkish officials have voiced concerns that he was murdered in the consulate. He had been living since past year in the U.S.in a self-imposed exile, in part due to the rise of Prince Mohammed, the son of King Salman.
"Consulate officials can not save themselves by saying that he left the building", Mr Erdogan told a news conference on Monday. Then why do you not prove this?
No evidence has been presented.
The Saudi ambassador to Washington, Prince Khalid bin Salman, who is also the brother of Crown Prince Mohammed bin Salman, denies these claims. "We have nothing to hide", in the interview published Friday.
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".
"See when I hear arrest of a friend who did nothing that is worth to be arrested, make me feel I shouldn't go".
The US president told reporters on Monday: "Hopefully that will sort itself out. Right now nobody knows anything about it".
U.S. President Donald Trump, in the first expression of concern by his administration on Khashoggi's disappearance, said he was troubled by reports about the journalist's fate.
When was he last seen?
The journalist was visiting the consulate in Istanbul to get documents which show he has divorced his wife so that he could go ahead with marrying his Turkish fiancee.
Turkish President Recep Tayyip Erdogan, left, chats with Hungarian President Janos Ader as he steps out on the terrace of the presidential Alexander Palace in Budapest, Hungary, Oct. 8, 2018.
Khashoggi, 59, had a long career as a senior journalist in Saudi Arabia and also as an adviser to top officials. Erdogan has said he would await the results of an investigation.
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The allegations of what the Saudi authorities may have done to one of their most prominent critics are - if proven - horrific. His fiancée waited outside the consulate for hours without hearing from him. "I can not believe that he has been killed.!"
The board said Saudi Arabia has to identify the 15 officials who were at the consulate and exactly what happened inside.
The worrying thing is, we may never know.
What have the Saudis said?
Turkish police were limited to footage from two street cameras that monitor the street outside the consulate after Saudi officials claimed that security cameras inside the consulate were not working at the time of last week's incident.
According to pro-government daily Sabah, the team arrived in Istanbul on two private planes, one which landed after 0300H (0000 GMT) on Tuesday while the second plane landed around 1700H (1400 GMT) after Khashoggi entered the consulate.
Meanwhile, Britain urged the Saudi government to explain what happened.
Erdogan's comments were his most direct suggestion yet about potential Saudi culpability in Khashoggi's disappearance.
In a March 6 Guardian editorial co-authored with Robert Lacey, he wrote: "For his domestic reform programme, the crown prince deserves praise".
Khashoggi, at the time of his disappearance, was working for the Washington Post and writing nearly regularly under the "Global Opinion" column.
Khashoggi is a familiar face on political talk shows on Arab satellite television networks and used to advise Prince Turki al-Faisal, former Saudi intelligence chief and ambassador to the United States and Britain.
MBS, as the crown prince is known, has been trying to bring Saudi Arabia into the 21st century.