"I'll say what we said consistently," Pompeo said of Khashoggi's murder.
"The position of the United States both privately and publicly is the same. It was an unreasonable act, an unacceptable murder. We are determined to do so. We are determined to know the facts as quickly and as completely as possible," he continued in an interview he lost with CBS "Face nation."
The resolution said the Senate "considers Crown Prince Mohammed bin Salman responsible for the killing of Jamal Khashoggi" and "calls on the Government of the Kingdom of Saudi Arabia to ensure appropriate accountability for all those responsible for Jamal Khashoggi's murder."
In his CBS interview said Pompeo USA "worthy of human rights worldwide" and called the killing of Khashoggi "outrageous". He added that the United States will "hold those responsible in charge".
"And then we'll talk about all the important things we do with the Kingdom of Saudi Arabia and all the support they give to keep Americans in Kansas and Colorado and California and in Washington, DC, safe," added Pompeo.
Pompeo earlier told Al Arabiya that he was going to Saudi Arabia from Sunday.
When asked if it was a partnership or a friendship with Saudi Arabia, he told Al Arabiya: "Call what you want. They have been great partners in the missions we have asked them to help us with. [1
CNN's Clare Foran, Ted Barrett, Kevin Bohn and Manu Raju contributed to this report.