He had reached the consulate to secure documentation for a forthcoming marriage, according to his fiancée, who waited outside.
His disappearance and reported murder in Istanbul "sends a petrifying signal to peaceful dissidents and critics that they are at risk even outside the country, and that the authorities are targeting them one by one wherever they can do so", said Lynn Maalouf, the director of Middle East Research at Amnesty International.
"God willing, we will not be faced with a situation we do not want".
Mr Erdogan was more circumspect, saying on Sunday he remained "positive" and would await the results of an investigation as Turkish authorities continue to look at camera footage and airport arrivals and departures.
Turan Kışlakçı says they would "react" if Khashoggi was killed by Saudi officials and said he hoped the "conscience of the worldwide community would react too".
Saudi Arabia said the allegations were baseless. A Saudi delegation had arrived in Istanbul to assist with the investigation, the statement said.
He later took up a position as a columnist with the Washington Post where he would regularly take aim at Saudi Arabia's conduct in Yemen's civil war as well as the policies of the Crown Prince.
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Mourinho added: "As a friend of mine was saying to me this morning, if tomorrow rains in London it's my fault". I think, to be honest with you, I'm furious.
His criticisms appeared in both the Arab and Western press.
The former government adviser, who turns 60 on October 13, has lived in the United States since past year to avoid possible arrest.
Meanwhile, Yasin Aktay, a deputy chairman of Turkey's ruling AK Paety told broadcaster CNN Turk that Khashoggi had not left the consulate in "normal ways". The case would not go unsolved, Aktay said.
He added that he still hoped the reports of his friend's death were untrue. Relations were already strained after Turkey sent troops to the Gulf state of Qatar a year ago in a show of support after its Gulf neighbors, including Saudi Arabia, imposed an embargo on Doha.
"Jamal was - or, as we hope, is - a committed, courageous journalist", the newspaper's editorial page editor Fred Hiatt said in a statement. "He writes out of a sense of love for his country and deep faith in human dignity and freedom", Hiatt said in a statement on the USA newspaper's website.
Erdogan said he was personally following the issue, without saying what he believed had happened to Khashoggi.
That relationship is already strained over several issues, including Turkey's support for Qatar in the blockade by Saudi Arabia; its closeness to the Muslim Brotherhood - blacklisted by Riyadh as a terrorist organisation; and its rapprochement with Saudi Arabia's arch-rival Iran.
MBS, as the crown prince is known, has been trying to bring Saudi Arabia into the 21st century. "Their foreign policy is based on a single doctrine: establishing the supremacy of Saudi Arabia in order to make it the sole arbiter of Arab affairs and the main point of entry for all global powers into the region", wrote Madawi al-Rasheed, a Britain-based academic and critic of the Saudi government, in a new collection of essays on the kingdom.
Khashoggi, 59, is a former government advisor who has criticised some of Prince Mohammed's policies and Riyadh's intervention in the war in Yemen.