Mr Khashoggi, a Saudi national, was last seen visiting the Saudi consulate in Istanbul on Tuesday.
A Turkish official told the BBC that initial investigations indicated he was murdered there.
Saudi Arabia has denied the accusations, saying it is “working to search for him”.
Mr Khashoggi has contributed articles to the Washington Post’s opinion section. The Post said it would be a “monstrous and unfathomable act” if he had been killed.
An official of Turkey’s ruling AK Party told broadcaster CNN Turk there was concrete evidence in the case, although none has yet been presented.
When was he last seen?
Jamal Khashoggi went to the consulate on Tuesday to obtain a document certifying he had divorced his ex-wife, so that he could marry his Turkish fiancée, Hatice Cengiz.
Ms Cengiz said she waited outside for 11 hours, but he did not come out.
She said Mr Khashoggi was required to surrender his mobile phone, which is standard practice in some diplomatic missions. He told her to call an adviser to Turkish President Recep Tayyip Erdogan if he did not return.
“Jamal is not dead. I cannot believe that he has been killed…!” Ms Cengiz wrote in a Twitter post that included a photo of Mr Khashoggi. She added that she was waiting for official confirmation as the allegations circulated…