Turkish officials have said they believe Khashoggi, 59, a critic of the Saudi leadership and a contributor to the Washington Post's Global Opinions section, was killed by a team of 15 Saudis flown in specifically to carry out the attack. Saudi authorities have called the charges "baseless."
The incident has angered rights activists and press freedom advocates, who have called on the Saudi Government to clarify Khashoggi's whereabouts. It has also raised tensions between regional rivals, Turkey and Saudi Arabia.
Turkey has yet to make any evidence public. The private Turkish broadcaster, NTV, reported that police had requested access to the Saudi Consulate in Istanbul. It was unclear whether the police were granted access or if they would search the diplomatic mission in Istanbul's Levent district at a later date.
Another report in the daily newspaper Sabah said investigators were also focused on a convoy of diplomatic vehicles that departed from the consulate on the day Khashoggi vanished. A US official said that Turkish investigators believe Khashoggi was likely dismembered, removed in boxes and flown out of the country.
US President Donald Trump said that he is "concerned" about Khashoggi, although US officials have not issued a public demand for answers from ally Saudi Arabia.
The President was asked about the case as he returned to the White House after a speech in Florida.
"I am concerned about it," Trump said. "I don't like hearing about it. Hopefully that will sort itself out. Right now nobody knows anything about it, but there's some pretty bad stories going around. I do not like it."
The White House has not otherwise commented on Khashoggi's disappearance.
According to two officials, senior members of the Administration have asked Riyadh to clarify the whereabouts of Khashoggi.
In a meeting with the Washington Post's publisher, Fred Ryan, the Saudi ambassador to the United States said that it was "impossible" that such a crime could be covered up by consulate employees "and we wouldn't know about it."
The ambassador, Prince Khalid bin Salman, reiterated a statement made by other Saudi officials that video cameras at the consulate had not been recording on the day of Khashoggi's visit. The ambassador declined to discuss the matter further, instead saying, "We don't want to harm the investigation." He added, "Speculation does not help our mission."
Salman said that Khashoggi, who was once close to the ruling family in Saudi Arabia, had "always been honest." Khashoggi's criticism of the current Saudi leadership "has been sincere," adding that he had seen him personally over the past year and had even exchanged text messages with the missing journalist.
Khashoggi had entered the consulate to obtain a document related to his upcoming wedding, according to his fiancee, Hatice Cengiz.
She waited outside for hours and called the police when he did not emerge. Khashoggi had been living in self-imposed exile in the United States since 2017, when he fled Saudi Arabia for fear of arrest.