Although Riyadh said that Saudi Crown Prince Mohammad bin Salman had nothing to do with Khashoggi's death, that claim has been met with skepticism.
Trump last week pulled Mnuchin from attending an economic summit in Riyadh this week that was being hosted by the crown prince, but the Treasury secretary still plans on attending an anti-terrorism summit in Saudi Arabia later this month.
Adel al-Jubeir told Fox News on Sunday that those responsible will be held accountable for "this huge and grave mistake".
Nebraska GOP Sen. Ben Sasse said in a separate interview on the same program that the United States needed to look at a wide range of responses to Saudi Arabia, including potentially cutting arms sales to the kingdom.
Trump sought to justify his muted response by pointing out the incident occurred in Turkey and that Khashoggi, a US resident and columnist for the Washington Post, was "not a United States citizen".
Saudi said Jamal Khashoggi was killed in a "brawl and fist fight" inside its consulate in Istanbul. It also said 18 people had been arrested as part of the case.
In a statement on Friday night, White House press secretary Sarah Huckabee Sanders said the USA will closely follow worldwide investigations into Khashoggi's death and will advocate for justice that is "timely, transparent and in accordance with all due process".
Turkish sources say the authorities have an audio recording purportedly documenting Khashoggi's murder inside the consulate.
Saudi Arabia's foreign debt has also been pressured, with yields rising across the country's dollar bond curve.
At the same time, Peter Navarro, Trump's White House trade chief and architect of his "Buy American" policy to ease restrictions on foreign arms sales, was stressing the importance of Saudi weapons deals and the implications for U.S.jobs, another administration official told Reuters.
"WAN-IFRA vehemently condemns the growing culture of impunity for crimes against journalists with which Saudi officials presumably believed they would be protected by".
Though Trump said Riyadh's account was credible, it drew doubt from some USA lawmakers.
That explanation has sparked allegations of a cover-up meant to shield the powerful crown prince.
The announcement on Sunday by Turkish President Recep Tayyip Erdogan that he will "go into detail" about the Khashoggi case in a speech in parliament heightened hopes for some clarity in a case that has been shrouded in mystery, conflicting accounts and shocking allegations.
While Corker said he does believe that Khashoggi, a Washington Post journalist, was "purposefully murdered" in a Saudi operation directed by the Crown Prince, he says he still wants to see a completed investigation.
President Trump appeared to initially accept the Saudi explanation, but US lawmakers, intelligence officials and foreign policy experts quickly accused the government in Riyadh of a coverup.
The United Kingdom Foreign Office described it as "a awful act" and said the people behind the killing "must be held to account".
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