"The Saudi authorities have notified that they are open to cooperation in this regard and that the examination can be conducted in their consular buildings in Istanbul".
The announcement came as a surveillance image surfaced of Jamal Khashoggi walking into the Saudi Consulate in Istanbul, just before he disappeared.
Turkish President Recep Tayyip Erdogan has called on Saudi Arabia to prove he left the consulate alive.
He said it comes as no surprise that Riyad is looking to quash criticism, but this case is beyond the sad but true usual jailing of journalists. Not only do they not know what happened to him, they say, but they are also anxious for his safety. Turkish employees of the residence had unexpectedly been told not to report for work that day, the newspaper said.
Britain urged the Saudi government to explain what happened.
"Violence against journalists worldwide is going up and is a grave threat to freedom of expression".
The Turkish ministry didn't say when the premises would be searched, prompting some experts to question the usefulness of the process.
Bin Salman said late on Friday that he was ready to allow Turkey to search the Saudi consulate in Istanbul for the missing journalist.
Mr Khashoggi, 59, went missing while on a visit to the consulate in Istanbul for paperwork to marry his Turkish fiancée.
Trump added that he hadn't spoken to Saudi officials on the matter, but was planning to "at some point".
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"If the search is carried out a week after the incident, everyone knows that all traces would have been cleared by now", Turkish political scientist Ahmet Kasim Han told DW. When asked if Khashoggi faced charges in Saudi Arabia, Salman said it was first important to discover where he was. It would make it more hard for the two governments to come up with a face-saving story blaming Khashoggi's disappearance on some third party, on rogue elements of the Saudi security forces, or on an accident during an interrogation that went wrong.
On Monday President Trump said that he was "concerned" about reports on Khashoggi's disappearance.
"Perhaps I'm simply trying to hide from the thought that I have lost a great man whose love I had earned".
United Nations spokeswoman Ravina Shamdasani said the "apparent enforced disappearance" of Khashoggi is a matter of "deep concern" to the human rights office in a press conference in Geneva on Tuesday.
Mr Trump has repeatedly lashed out at the media, calling it the "enemy of the people", and has raised human rights prominently only when pressuring USA antagonists such as Iran and China.
The rights group Prisoners of Conscience, which is an independent non-governmental organization advocating human rights in Saudi Arabia, announced in a post on its official Twitter page that it did not dismiss the possibility that Khashoggi's sudden disappearance was an attempt to silence the writer.
The hit squad finished the murder operation within two hours and departed Turkey for various countries, said the Times' source, citing information from "top Turkish officials". He used to advise Prince Turki al-Faisal, former Saudi intelligence chief and ambassador to the United States and Britain.
Khashoggi has been an outspoken critic of the Saudi government, causing him to leave his home country previous year to live in exile in the United States.
Mr Erdogan was more circumspect, saying on Sunday he remained "positive" and would await the results of an investigation as Turkish authorities continue to look at camera footage and airport arrivals and departures.