Meanwhile, Turkish President Recep Tayyip Erdogan has said Saudi Arabia must prove Khashoggi left their building alive. He was also a vocal critic of the Saudi Arabian government and fact that Riyadh has taken a harsh approach to members of the press who criticize the country's leadership lends some credence to the allegations of murder or imprisonment. "So until they resolve that we aren't going to know the details", he added. "We have some concrete information, it won't be an unresolved crime", the Middle East Eye reported.
Britain urged the Saudi government to explain what happened.
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". The ministry did not say when the premises would be searched. 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.
Turkish officials have said that Khashoggi was murdered inside the consulate.
There was no immediate comment on the report from the Saudi authorities.
Turkey's government hasn't provided evidence after a spate of anonymous allegations that the Saudi writer was killed inside the Istanbul consulate.
"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.
That Saudi Arabia would allow foreigners to enter a consulate and search it shows the growing worldwide pressure the kingdom faces over the disappearance of Mr Khashoggi, a critic of Saudi Arabia and contributor to the Washington Post.
The Washington Post contributor, who has penned articles critical of some of Saudi Crown Prince Mohammed bin Salman's policies in the Arab and Western press, vanished a week ago.
The disappearance of the 59-year-old journalist has sparked global concern for his welfare.
"At this time, I implore President Trump and first lady Melania Trump to help shed light on Jamal's disappearance", she said.
"Just spoke to Senators Bob Corker and Ben Cardin about our shared concerns regarding the whereabouts and treatment of Mr Jamal Khashoggi", Republican Senator Lindsey Graham tweeted Monday.
"Perhaps I'm simply trying to hide from the thought that I have lost a great man whose love I had earned".
Sen. Bob Corker (R-TN), for one, was at least calling for an explanation from the Saudis on Tuesday, which Trump had failed to do.
He said police were examining CCTV footage of entrances and exits at the consulate and Istanbul airport.
After several of his friends were arrested, his column was cancelled by the al-Hayat newspaper and he was allegedly warned to stop tweeting, Mr Khashoggi left Saudi Arabia for the USA, from where he wrote opinion pieces for the Washington Post and continued to appear on Arab and Western TV channels.
The Saudi government, he said, was "fully cooperating" in the Turkish government's investigation. Saudi Arabia still insists it's all baseless.
Khashoggi previously had close links with the Saudi royal family, including having served as a media aide to Prince Turki al-Faisal, when the latter was director general of the Saudi intelligence agency.
Karen Elliott House, a veteran writer on Saudi affairs and chairwoman of the board of trustees at RAND Corp., said USA support for the Yemen war is likely to be the focus of congressional criticism but won't endanger a relationship that has endured for decades, underpinned by shared strategic interests.
He had been living since previous year in the United States, in a self-imposed exile, in part due to the rise of Prince Mohammed, the son of King Salman.