Global concern over the case has led to many business and political figures pulling out of an upcoming conference in the Saudi capital, Riyadh.
The four organizations said an worldwide investigation should probe Saudi Arabia's role and aim to identify everyone responsible for ordering, planning and executing any operations related to Khashoggi's disappearance.
"But it may cause them to limit some of the excesses that we have seen recently".
US Secretary of State Mike Pompeo was sent to Riyadh on Tuesday, according to the administration, to press the Saudi leadership to get to the bottom of the case.
Earlier, they spent almost nine hours in the Saudi consul's residence along with Saudi investigators.
"We made clear to them that we take this matter very seriously", Pompeo said.
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Authorities widened the geographic focus of the search after tracking the routes and stops of cars that left the Saudi consulate and the consul's residence on October 2, the day Khashoggi was last seen, the senior officials said.
Mr. Trump said he would wait for the results of three different investigations before drawing conclusions.
Writing on Twitter, after meeting President Trump and Pompeo, Mnuchin said, "we have decided I will not be participating". Khashoggi has not been seen since he entered the Saudi consult in Istanbul more than two weeks ago and is feared dead.
In Istanbul, a leaked surveillance photo showed a man who has been a member of the crown prince's entourage during trips overseas walking into the Saudi Consulate just before Mr Khashoggi vanished there. "I know what I'm going to do and I'm going to sanction the hell out of Saudi".
Turkish officials allege Mr Khashoggi was murdered inside the consulate by Saudi Arabian agents - but the Kingdom denies the charges.
Saudi Arabia's Future Investment Initiative, dubbed "Davos in the Desert", will be missing numerous major players after several world leaders and top business executives have decided not to attend.
Leading human rights and journalists' organisations have urged Turkey to ask the United Nations to launch an investigation into the disappearance and "possible extrajudicial execution" of Mr Khashoggi.