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6 year oldUS Treasury Secretary Steven Mnuchin met Mohammed bin Salman on Monday.
Turkish officials say Khashoggi was murdered in the Saudi consulate in Istanbul after a visit on 2 October.
Saudi officials have given a series of conflicting accounts, but now say a "rogue operation" was to blame.
They initially said Khashoggi had left the consulate on the same day he visited it. Last Friday they admitted for the first time he was dead and said he had been killed in a "fist fight".
Turkish President Recep Tayyip Erdogan has said he will reveal the "naked truth" of the matter in parliament on Tuesday.
Saudi state media reported that Mr Mnuchin and the crown prince had stressed "the importance of the Saudi-US strategic partnership".
The meeting in the Saudi capital was held behind closed doors and the US has so far made no public comment on the talks.
They were held despite the fact that Mr Mnuchin - like a number of other Western politicians and businessmen - had pulled out of a major investment forum being held in the Saudi capital this week.
President Donald Trump's latest comment suggests the US is yet to decide on its response.
"I am not satisfied with what I've heard," Mr Trump told reporters at the White House.
But he added: "I don't want to lose all that investment that's been made in our country," referring to the multi-billion-dollar arms deals with Saudi Arabia.
He said: "We're going to get to the bottom of it."
Mr Trump also said he had discussed the issue with the Saudi crown prince, seen as the country's most powerful figure.
The Saudis say they have arrested 18 people, sacked two aides of Mohammed bin Salman and set up a body, under his leadership, to reform the intelligence agency over the killing.
Foreign Minister Adel al-Jubeir provided the latest comments, saying the killing was a "rogue operation".
"We are determined to find out all the facts and we are determined to punish those who are responsible for this murder," he said.
"The individuals who did this did this outside the scope of their authority," he added. "There obviously was a tremendous mistake made, and what compounded the mistake was the attempt to try to cover up."
He said that Saudi Arabia did not know where the body was.
Mr Jubeir insisted that the action had not been ordered by the crown prince.
However, Yeni Safak, a media outlet close to Turkey's government, said it had information showing that the office of the crown prince received four phone calls from the consulate after the killing.
Reuters news agency reported on Sunday it had spoken to a Saudi official who said Khashoggi had died in a chokehold after resisting attempts to return him to Saudi Arabia. His body was then rolled in a rug and given to a local "co-operator" to dispose of.
A Saudi operative then reportedly donned Khashoggi's clothes and left the consulate.
CNN quoted a senior Turkish official as saying a Saudi agent had been captured on surveillance footage dressed as the journalist.
The video appears to show the man leaving the consulate by the back door on the day the journalist was killed, wearing Khashoggi's clothes, a fake beard and glasses, CNN said.
In another development, Turkish police found a car belonging to the Saudi consulate left in an underground car park in Istanbul.
Turkish media also posted footage apparently showing Saudi consular staff in Istanbul burning documents a day after Khashoggi's disappearance.
Analysis by BBC security correspondent Frank Gardner
After weeks of calculated and often lurid leaks to the Turkish media, Tuesday morning's statement by President Erdogan is eagerly awaited.
Turkey has promised "a full account" of what happened to Khashoggi, with nothing held back.
So that would include the widely reported audio tape from inside the Saudi consulate then? And evidence of the "bone saw" allegedly brought in by the hit team that killed him?
Because both of these elements are crucial in establishing the facts about what happened and the motives of his murderers. If evidence of the bone saw can be produced then it would certainly imply murderous intent by the hit team from Riyadh.
The audio tape of his murder - if it does exist - could be excruciating to listen to - but is an essential part of the puzzle of how Khashoggi died. But Turkey, a country that has itself jailed more journalists than any other nation on Earth, may have its own reasons for holding back on what it has.
For the full story, we may have to wait a little longer yet.
Many of them have condemned the murder and demanded a full investigation:
But several of Saudi Arabia's regional allies - including Kuwait and Egypt - have come out in its support.
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