The journalist, who writes opinion pieces for the Post, has been critical of some policies of Saudi Crown Prince Mohammed bin Salman and Riyadh's intervention in the war in Yemen.
"Jamal and I have not seen eye to eye on many issues but having him go missing like this is bad", he said.
Khashoggi, a familiar face on political talk shows on Arab satellite television networks for years, has lived in self-exile in Washington for more than a year after he said the authorities had instructed him to stop tweeting.
They said the Saudi envoy was called in on Wednesday to clarify the whereabouts of Khashoggi, a critic of Riyadh's foreign policy and its crackdown on dissent who left Saudi Arabia past year saying he feared retribution for his views.
When Khashoggi entered the consulate on Tuesday afternoon, he left his phone with his fiancee, along with instructions that she should call an adviser to President Erdogan if he did not return, she said.
Turkey has supported the Gulf state of Qatar in its prolonged stand-off with Saudi Arabia and its allies, sending troops to Qatar past year. "We do not have information revealing the contrary", he said.
"According to the information we have, this person who is a Saudi citizen is still at the Saudi Consulate in Istanbul", he said.
"The Post is extremely concerned about Jamal", Post editor Fred Hiatt said.
"I do not know what has happened to him".
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 U.S., from where he wrote opinion pieces for the Washington Post and continued to appear on Arab and Western TV channels. "We hope the problem will be solved smoothly", he said.
Turkey summoned the Saudi ambassador to its Foreign Ministry on Thursday over the writer's disappearance, said an official who requested anonymity in line with government rules.
A USA state department spokesperson said they had seen the reports from Istanbul and were "seeking more information at this time".
He is also known for his close association with the young Osama Bin Laden, with whom he travelled extensively in Afghanistan in the 1980s during the Soviet occupation - though he publicly rejected Bin Laden's later ideologies and had lost touch with him long before the 2001 attacks on the US.
Formerly an editor of the Al-Watan newspaper and of a short-lived Saudi TV news channel, Khashoggi has also been a contributor to BBC programmes about Saudi Arabia and the Middle East. The channel stayed on the air for less than 11 hours before being shut down.
Turkey has had strained relations with Saudi Arabia and other Gulf Arab states since June, 2017, when Ankara stood by Qatar in a regional row.
Khashoggi himself advocated for more social freedoms in the kingdom in his columns at the Post.
The statement released by the state-run Saudi Press Agency did not elaborate.
His fiance said Khashoggi visited the consulate to obtain some documents in order to be married next week.
Saudi Arabia has stepped up its crackdown on human rights campaigners and activists over the past couple of years.
Kavanaugh a step closer to lifetime Supreme Court post after Senate vote
Steve Daines to stay at his daughter's wedding in his home state instead of flying to Washington to cast his supporting vote. It just may be that in my view he's not the right man for the court at this time", Murkowski told reporters on Capitol Hill.