Certain areas of the consulate were to remain off-limits, although officials would be able to inspect surveillance cameras, Turkish media reported.
Khashoggi was living in self-imposed exile in the United States and had criticized Saudi Crown Prince Mohammed bin Salman in columns written for The Washington Post.
In protest of Khashoggi's disappearance, several US businesses leaders have pulled out of next week's Future Investment Initiative in Riyadh, dubbed "Davos in the Desert", after the annual meeting of world economic interests in Switzerland.
The three executives' companies have significant financial ties to Saudi Arabia. Prince Mohammed told Reuters past year that Blackstone and BlackRock Inc were planning to open offices in the kingdom.
Saudi Arabia has already delved into the world of sport with purchases in both F1 and WWE - and football is already part of a wider political battle between the Gulf States. The alleged slaying threatens to derail efforts by Saudi Crown Prince Mohammed bin Salman to portray Saudi Arabia as a more open and tolerant place to visit, invest in and do business.
Executives from media, technology and financial firms have in the last few days withdrawn from the conference, scheduled for October 23-25, after the disappearance of Saudi journalist Jamal Khashoggi.
The Foreign Office spokesman responding to a query about Pakistan's stance on the issue said "we understand that the investigation was ongoing and it would therefore be appropriate to await the outcome".
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It listed $6.9 billion in assets and $11.3 billion in liabilities in documents filed in the bankruptcy court, Reuters reported . Lampert, the company's largest shareholder, has stepped down as CEO but will remain chairman of the board.
Three high-profile Wall Street CEOs reportedly attempted to persuade Saudi officials to push back Saudi Arabia's Future Investment Initiative conference.
A Saudi source said on Monday that the Crown Prince has ordered an internal investigation of the disappearance.
Turkey said Mr Erdogan "stressed the forming of a joint working group to probe the case".
Saudi officials had reportedly resisted allowing Turkish police into the consulate after learning that investigators planned to use Luminol, a forensic chemical that reveals bloodstains even if they have been washed clean.
It is not clear what kind of search the officials will conduct and whether it will include a forensic examination, given that it has been nearly two weeks since the reporter was last seen. Earlier Monday, a cleaning crew with mops, trash bags and what appeared to be bottles of bleach walked in past waiting journalists.
It was unclear on Tuesday when or if Saudi Arabia would go public with any new admissions in relation to Khashoggi's disappearance.
Turkish sources allege he was killed by a 15-strong team of Saudi agents but Riyadh insists that he left the consulate unharmed.
If the autopsy specialist left Saudi Arabia for Istanbul before Khashoggi entered the consulate, as Turkish sources have asserted, it might be hard to square with the explanation that any killing was the result of a botched interrogation, and not premeditated.