The consulate insists the writer left its premises, contradicting Turkish officials.
In contrast, a Saudi official quoted by Reuters news agency said the journalist was "not in the consulate nor in Saudi custody".
"As we speak today, there [are] Saudi intellectuals and journalists jailed".
Khashoggi's disappearance threatens to further harm relations between Turkey and Saudi Arabia, which are on opposite sides of an ongoing four-nation boycott of Qatar and other regional crises.
"If Saudi authorities surreptitiously detained Khashoggi it would be yet another escalation of Crown Prince Muhammad bin Salman's reign of repression against peaceful dissidents and critics", Human Rights Watch Middle East director Sarah Leah Whitson said in a statement.
Turan Kislakci, one of Khashoggi's friends, said it is suspected that he was moved from the consulate and that the Saudi and Turkish governments were negotiating a face-saving way for the Saudis to release him. "To do otherwise would betray those who languish in prison".
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Khashoggi, a 59-year-old veteran journalist who has lived in self-imposed exile in the US since Prince Mohammed's rise to power, disappeared Tuesday while on a visit to the consulate to get paperwork done to be married to his Turkish fiancée. "We believe something is up and they won't tell us", said the official, who spoke on the condition of anonymity to discuss private diplomatic conversations. He entered the building of the consulate, he has to come out of there safe and sound. As details begin to transpite, it turns out the September 30 meeting between Saudi Crown Prince Mohammad bin Salman and Kuwaiti Emir Sheikh Sabah al-Ahmad al-Jaber al-Sabah has sowed more confusion than settled discrepancies between the two nations.
A spokesman for Turkish President Recep Tayyip Erdogan told reporters on Wednesday night that authorities believed the journalist was still there.
A group representing Turkish-Arab journalists on Friday voiced solidarity with one of their own who is missing, fate unknown. Waves of arrests over the past year have swept up religious figures, business executives and, most recently, Saudi Arabia's most active women's rights advocates.
Notably, Khashoggi would not be the only Gulf national to have been arrested overseas to be returned to the kingdom, and other incidents have been far more public. Over a long career, he has had close contact with Saudi royalty and knows more than most about how they think and function. For instance, Nawaf Talal al-Rasheed, a Qatari national and a cousin of famed Saudi academic and critic Madawi al-Rasheed, was arrested in Kuwait and passed to Saudi authorities "under bilateral mutual security arrangements between Kuwait and Riyadh".