Saudi Arabia's consulate in Istanbul insists a prominent journalist critical of the Saudi government had already left its building before he vanished.
The consulate said it was "following up reports of the disappearance" of Jamal Khashoggi, who went there to complete paperwork on Tuesday.
Khashoggi's fiancée accompanied him to the building, but she had to wait outside. She did not see him leave.
Turkish authorities have also said they believe Khashoggi is still there.
The Turkish foreign ministry summoned Saudi Arabia's ambassador on Wednesday and "asked for an explanation" about the disappearance, NTV television reported.
The ambassador informed Deputy Foreign Minister Yavuz Selim Kiran that he had no information about Khashoggi's whereabouts, but Mr Kiran told him that the issue "should be cleared up immediately", it added.
The US state department has also requested information about Khashoggi's whereabouts and expressed concern about his safety.
The 59-year-old journalist had been living in self-imposed exile in the US since last year, when he left the Gulf kingdom after criticising the policies of Saudi Crown Prince Mohammed bin Salman.
He is a regular contributor to the Washington Post, which said it had "reached out to anyone we think might be able to help locate him".
What happened on Tuesday?
Khashoggi went to the consulate to obtain a document certifying he had divorced his ex-wife, so that he could marry his Turkish fiancée, Hatice.
She said that he was "stressed and sad" that he was forced to go to the building.
Khashoggi was required to surrender his mobile phone, which is standard practice in some diplomatic missions. Hatice said he left the phone with her and told her to call an adviser to Turkish President Recep Tayyip Erdogan if he did not return.
Hatice said she waited for Khashoggi outside the consulate from about 13:00 (10:00 GMT) until after midnight and did not see him leave. She returned when the consulate reopened on Wednesday morning.
What does Saudi Arabia say?
A Saudi official confirmed on Wednesday that Khashoggi had visited the consulate to complete paperwork, but said he had "exited shortly thereafter".
"He is not in the consulate nor in Saudi custody," the official added.
On Thursday, the official Saudi Press Agency cited the consulate as saying it was "carrying out follow-up procedures and co-ordination with the Turkish local authorities to uncover the circumstances of the disappearance of Jamal Khashoggi after he left the consulate building".
What does Turkey think?
Turkish presidential spokesman Ibrahim Kalin told reporters on Wednesday: "According to the information we have, this person who is a Saudi citizen is still at the Saudi consulate in Istanbul."
"We don't have information to the contrary," he added.
The head of the Turkish-Arab Media Association told the New York Times that Turkish police officers providing security for the consulate had checked their security cameras and did not see the journalist leave on foot. But Turan Kislakci added that diplomatic cars had been seen moving in and out.
The BBC's Mark Lowen says the mystery threatens to deepen the strains in the relationship between Turkey and Saudi Arabia.
Turkey has taken the side of Qatar over its blockade by Saudi Arabia and other neighbours, and Turkey's rapprochement with Iran has riled the government in Riyadh, our correspondent adds.
Why might Saudi Arabia want to hold Khashoggi?
He is one of the most prominent critics of the crown prince, who has unveiled reforms praised by the West while carrying out an apparent crackdown on dissent, which has seen human and women's rights activists, intellectuals and clerics arrested, and waging a war in Yemen that has triggered a humanitarian crisis.
A former editor of the al-Watan newspaper and a short-lived Saudi TV news channel, Khashoggi was for years seen as close to the Saudi royal family. He served as an adviser to senior Saudi officials.
After several of his friends were arrested, his column was cancelled by the Al-Hayat newspaper and he was allegedly warned to stop tweeting, Khashoggi left Saudi Arabia for the US, from where he wrote opinion pieces for the Washington Post and continued to appear on Arab and Western TV channels.
"I have left my home, my family and my job, and I am raising my voice," he wrote in September 2017. "To do otherwise would betray those who languish in prison. I can speak when so many cannot."