In contrast, Turkish media have reported that Turkish investigators have evidence, including recordings, that Khashoggi was tortured, killed and dismembered by a Saudi hit squad sent to the consulate ahead of his arrival.
President Donald Trump said the 18 arrests by Saudi Arabia is a "good first step" and "a big step".
Khashoggi reportedly was killed inside the Saudi consulate in Istanbul on October 2. Saudi officials previously denied any knowledge of his whereabouts and claimed the journalist had left the consulate alive.
US Senator Lindsey Graham, a Republican from SC, has been sharply critical of Saudi Arabia after the disappearance of Khashoggi on October 2.
The Saudi statement confirming the death of Khashoggi in a fist fight did not appear to be credible for some USA lawmakers, who demanded that Riyadh be held accountable for the incident.
It called on Saudi authorities to produce Khashoggi's body so that independent forensic experts could perform an autopsy. "We have nothing to hide", says the crown prince.
Trump has warned there would be "very severe" consequences if Saudi Arabia is behind the disappearance of the journalist, but Pompeo said, "I'm not going to get into what those responses might be".
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"People fear them. You challenge them, you might end up in prison, and that has happened", he said.
"We are not accusing anyone in advance but we don't accept anything to remain covered (up)", said ruling Justice and Development Party spokesman Omer Celik.
Earlier Saturday, a statement from the Saudi public prosecutor carried by Saudi state TV said 18 Saudi nationals have been arrested so far in connection with Khashoggi's death.
German Chancellor Angela Merkel said the "horrific events" surrounding Khashoggi's killing "still haven't been cleared up and of course we demand that they be cleared up".
President Recep Tayyip Erdogan has vowed to uncover the truth behind Saudi journalist Jamal Khashoggi's killing, sources close to the Turkish leader have told Middle East Eye, as global outrage over Riyadh's most recent explanation grows.
In a recent off-the-record interview published posthumously by U.S. magazine Newsweek, Khashoggi described the 33-year-old crown prince as "an old-fashioned tribal leader" but said he would have accepted an offer to work as his adviser.
Turkish officials have coordinated sustained leaks of information to local and U.S. media that suggest Khashoggi was tortured and murdered and his body dismembered with a bone saw.
Were his remains to be found, traces of the drug may be found, asking new questions of Saudi Arabia's fist-fight narrative. But Pompeo, traveling in Mexico, told reporters, "I've seen no tape".
However, the admission, which came amid increasing pressure on Riyadh, has done little to ease worldwide demands for accountability.