Meanwhile on Tuesday, the Washington Post - where Khashoggi wrote columns after fleeing Saudi Arabia over fears of retribution for his critical commentary - reported U.S. intelligence intercepted communications of Saudi officials planning to abduct the prominent journalist.
Turkish and Saudi authorities have given conflicting accounts of Khashoggi's disappearance.
Turkey has summoned the Saudi ambassador to request the kingdom's "full co-operation" in an investigation into the disappearance of journalist Jamal Khashoggi, who Turkish officials say was killed while visiting the Saudi Arabian Consulate in Istanbul.
The Vienna Convention on diplomatic relations allowed for consulates to be searched by authorities of a host country with consent of the mission chief, he said.
Late last week, the Washington Post ran blank space where a column by dissident Saudi journalist Jamal Khashoggi, who wrote for its Global Opinions section, should have appeared.
A Turkish official told the Reuters news agency, "The initial assessment of the Turkish police is that Mr. Khashoggi has been killed at the consulate of Saudi Arabia in Istanbul".
Jamal Khashoggi's fiancee Hatice Cengiz said she believes he is still alive.
Turkish President Recep Tayyip Erdogan has called for Saudi officials to prove their contention that Khashoggi left the consulate, as most accounts say the last he was seen was entering the building.
While a military conflict is not likely to arise between Turkey and Saudi Arabia, this new development will place more strain on the relationship, further complicating the already hard situation in the Middle East. However, the consulate has other entrances and exits as well, through which Saudi officials insist he left.
"If he left, you have to prove it with footage".
The US president, Donald Trump, a robust ally of Saudi Arabia, who had pledged to stay out of the country's domestic affairs, made his first reference to the case on Monday, telling reporters he was "concerned" about "some pretty bad stories" about Khashoggi's fate. After a positive first meeting with consular staff, who welcomed him warmly and assured him that the necessary paperwork would come through, Jamal was hardly concerned ahead of his second visit.
Turkish authorities have claimed they have surveillance camera video of Khashoggi entering the consulate but never leaving.
The obvious difficulty of imposing ambitious reforms on the Kingdom led the administration to cut MBS some slack for heavy-handed tactics, but if Khashoggi was kidnapped or murdered by Saudi officers in Turkey (with his corpse dismembered to dispose of the evidence, according to the most lurid rumors in Turkish circles) it could become a major diplomatic crisis for the White House.
Flight data collected by AirNavRadarBox, a firm that tracks private and commercial planes all over the world, showed that the first of the two planes left Riyadh late October 1 and touched down in Istanbul the following day at 3:15am. That team was sent "specifically for the murder", a person with knowledge of the Turkish investigation tells the Post.
Riyadh has said Khashoggi left the consulate after his visit.
The search will take place as part of the official investigation, which was being conducted "in an intense manner", he said without giving any date. He served as an adviser to senior Saudi officials.
"Hopefully that will sort itself out", he added.
Mr Hunt said that if reports of Mr Khashoggi's death proved correct, the United Kingdom would regard the situation as "serious", adding: "Friendships depend on shared values". "I know nothing right now".