The prime minister also says Canada has "serious issues" around reports about the disappearance of US journalist Jamal Khashoggi, although he says there is still more to learn before he'll comment further.
Mr Trump has said his administration won a $110 billion military order from Saudi Arabia and that the deal, combined with Saudi commitments to invest heavily in the United States, was worth hundreds of thousands of U.S. jobs.
Separately, several global businesses have withdrawn from the upcoming Future Investment Initiative conference in Riyadh.
"We express concerns for Mr Khashoggi and his family", Mr Mnuchin said.
With the mystery over Jamal Khashoggi unresolved 11 days after he walked into the consulate and failed to reappear, a pro-government Turkish daily said the Saudi national had recorded his own interrogation inside the mission on an Apple Watch.
Khashoggi entered the Saudi consulate in Istanbul on October 2to get documents for his forthcoming marriage.
Turkish authorities say a team of Saudis killed Khashoggi, and U.S. intelligence intercepts show Saudi officials discussing an operation to lure Khashoggi - a Saudi citizen who had been living in the United States - back to Saudi Arabia from his home in Virginia and detain him.
In an interview with "60 Minutes," Mr. Trump said Saudi Arabia "vehemently" denies its involvement in the disappearance of Jamal Khashoggi, a Washington Post opinion page contributor who had lived in Virginia in exile and whose fiancée says he entered the Saudi consulate in Istanbul on October 2 and hasn't been seen since. the interview is set to air Sunday night.
Early on Saturday, the state-run Saudi Press Agency published a statement from Saudi Interior Minister Prince Abdulaziz bin Saud again denying the kingdom's involvement.
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He has also halted discussions about a $1bn ($NZ1.54b) investment by the Saudi sovereign wealth fund into Virgin's space ventures.
Also speaking on Friday's release of American pastor Andrew Brunson, Cavusoglu said he was released as the judicial process on Brunson was completed.
Government-backed Saudi Arabian media outlets are trying to portray the disappearance of prominent journalist Jamal Khashoggi as a "conspiracy" targeting the kingdom.
The audio recording in particular provides the most persuasive and gruesome evidence that the Saudi team was responsible for Khashoggi's death, the officials said. "If more information comes out and changes, we could look at that, but I am planning on going".
Saudi Arabia ended a 35-year ban on movie theaters with a screening of "Black Panther" in April.
"I'll tell you what I don't want to do".
Turkish and foreign media who have camped outside the consulate all week noticed the motorcade arriving on Friday but it had not been immediately clear who were the Saudi personnel entering the consulate were.
Separately, a video has emerged of men described as Saudi intelligence officers entering and leaving Turkey.
The Saudi delegation was in Turkey and due to have talks this weekend in Ankara and take part in a working group on the disappearance, official Turkish media said.