But questions remain, and most recently the Washington Post reported that Salman claimed in a phone call with us officials that Khashoggi was unsafe and a member of the Muslim Brotherhood, which Khashoggi's family denies.
More recently, Saudi authorities have said the murder was "premeditated", though the details and culpability remain unclear.
The New York Times, quoting two people familiar with the matter, reported Friday that White House officials knew from an October 9 phone call with Saudi Crown Prince Mohammed bin Salman that he considered Khashoggi a risky Islamist, and therefore knew the Saudi prince had a potential motive for the killing.
The statement is the clearest yet from the Turkish authorities about the fate of the Washington Post journalist, whose remains have not yet been found.
The Saudi government has said it will carry out a thorough and transparent investigation and that the suspects will be prosecuted in Saudi Arabia.
Killing an innocent person is one crime, the treatment and extent of what was done to the body is another crime and dishonour.
Fidan, the Istanbul prosecutor, on Wednesday said that Khashoggi was strangled shortly after entering the consulate and that his body was dismembered afterward.
Pompeo told a local radio station in St Louis that the United States had "deep and long-term strategic relationships" with Saudi Arabia and said "we intend to make sure that those relationships remain intact".
"The whole world has been shocked by this grotesque killing, and it's vital that we don't let the outrage fade away without justice being done", said Kate Allen, Amnesty International UK's director, in a statement.
There was no immediate comment on the report from Turkish officials.
Bin Salman has told President Donald Trump's son-in-law, Jared Kushner, to whom he is close, that low-level officials who had gone rogue had killed Khashoggi.
Khashoggi was killed on October 2 inside the Saudi consulate in Istanbul, where he had gone to obtain necessary papers for his upcoming wedding. "Then murderers in Turkey leave the country freely", Republican People's Party leader Kemel Kilicdaroglu said Thursday, speaking at the Pharmacy Congress.
The Turkish government, however, maintains that Khashoggi was assassinated by a hit squad sent from Saudi Arabia specifically for the task.
Prince Mohammad bin Salman, who has positioned himself as a Saudi reformer, has denounced the murder as "repulsive" and strongly denied any involvement.
A month on from Khashoggi's murder in the Saudi consulate in Istanbul, Erdogan said he did "not believe for a second" that King Salman was to blame.
"Of all nations, the United States should be leading the way in bringing the perpetrators to justice", Hatice Cengiz wrote.