The president said the consequences for Saudi Arabia, if they are ultimately deemed culpable, "will have to be very severe". His warning came as the administration toughened its response to a disappearance that has sparked global outrage.
Mnuchin's decision came after Pompeo returned from meetings in Saudi Arabia in recent days and said the US wants to give the government there "a few more days" to present the results of an investigation into the disappearance of Khashoggi.
Secretary of State Michael Pompeo said he expects Turkish and Saudi Arabian investigations to reveal a "complete picture" of what happened to Khashoggi.
The US president has been on the defensive ever since Khashoggi - a US resident and Washington Post contributor who had criticised Prince Mohammed - vanished on Oct 2 after visiting the Istanbul consulate.
Saudi Arabia's al-Arabiya broadcaster claimed the 15 men were "tourists".
"We continue to seek an interview with Crown Prince Mohammad bin Salman", the network said in a statement.
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Khashoggi , an outspoken critic of the regime, hasn't been seen since entering a Saudi consulate in Islamabad on October 2. BBC News report that a Turkish security source has video and audio proving Khashoggi was killed inside the consulate.
"It certainly looks that way to me", Trump told reporters at Joint Base Andrews when asked if Khashoggi was dead.
Saudi Arabia's Future Investment Initiative, a conference that is widely known as the "Davos of the Middle East", has provided a platform for business leaders and politicians to take a stand against the lack of information and transparency over what happened to Khashoggi.
At around 4:40 pm (1340 GMT) a team of a dozen police and prosecutors, including forensics experts in white overalls entered the residence of the consul, who was at the consulate when the alleged assassination of Khashoggi took place, according to Turkish media.
"I'm not giving cover at all", he said, adding that he would be getting a "full report" on the affair from Pompeo by the end of the week.
Pompeo briefed President Donald Trump on the issue and the talks he had this week with the leaders of Saudi Arabia and Turkey in this regard. The crown prince is next in line for the throne, which is held by his ailing, aged father King Salman.
And a senior United States official said Pompeo had warned the Saudi crown prince that his credibility as a future leader was at stake, reflecting the administration's concern about how the case could affect relations.