He wrote columns for the Washington Post and the Guardian.
Turkish Foreign Ministry spokesman Hami Aksoy said the investigation was "continuing intensively", and that the Vienna Convention allowed for consulates to be searched by the authorities of the host country with the consent of the mission chief.
The Turkish government is demanding access to the diplomatic facility to search it after allegations that Khashoggi had been chopped up inside the building and his body parts sent to Saudi in boxes, rocked Middle East relations.
Turkish officials told Reuters at the weekend they believed he had been killed inside the Saudi consulate.
According to The Washington Post, where Khashoggi was a contributor, he visited the Saudi consulate in Istanbul last week to get a document for his upcoming wedding. "Jamal has many friends in the Kingdom, including myself, and despite our differences, and his choice to go into his so called 'self-exile, ' we still maintained regular contact when he was in Washington".
"The worrying trend that we see is a crackdown on critical and independent journalism in Saudi and about Saudi", Robert Mahoney, Deputy Executive Director of CPJ, told CBS News' Pamela Falk.
The Saudi consulate called the claim "baseless" on Twitter.
In his first remarks about the disappearance, President Trump told reporters Monday afternoon that he was concerned.
Private broadcaster NTV reported on October 9 that all suspects were seen entering the consulate half an hour before Khashoggi and leaving it after nearly three hours. "We are trying to make certain that no innocent people die down there right now", he said.
Mr Khashoggi, who was living in self-imposed exile in the USA and working for the Washington Post before his disappearance, was a frequent critic of the kingdom's de facto ruler Crown Prince Mohammed bin Salman, whom he described as a "brash and abrasive young innovator" who was "acting like Putin". "He's a Saudi citizen and we are very keen to know what happened to him". Footage emerged Tuesday showing Khashoggi entering the building the week before. Khashoggi, a 59-year-old veteran journalist who has lived in self-imposed exile in the USA since Prince Mohammed's rise to power, disappeared October 2 while on a visit to the consulate to get paperwork done to be married to his Turkish fiancÃ©e.
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In July, the United Nations human rights office called on Saudi Arabia to release all peaceful activists, including women held for campaigning against a ban on driving as it was being lifted.
The Turkish president said in a speech to members of his Justice and Development Party that he was following Khashoggi's case himself.
Prince Mohammed earlier denied in an interview with Bloomberg that the journalist had been inside the consulate and said Turkish authorities could search the building, which is Saudi sovereign territory.
Two Turkish sources also confirmed Khashoggi's death, stressing he was killed inside the consulate.
U.S. President Donald Trump said on Tuesday he plans to speak with the Saudis without elaborating.
The Khashoggi case puts the Trump administration unexpectedly on the side of Turkey, where two top government officials have been slapped with United States sanctions over the detention of an American pastor.
"Do you not have cameras and everything of the sort?"
Khashoggi was once a Saudi newspaper editor and is a familiar face on political talk shows on Arab satellite television networks. "I said nothing. I didn't want to lose my job or my freedom".
Khashoggi, 59, had a long career as a senior journalist in Saudi Arabia and also as an adviser to top officials.