Appearing on CBS' Face the Nation, Pompeo told host Margaret Brennan he would raise the issue of holding Khashoggi's killers accountable with the crown prince during his visit to the Saudi capital of Riyadh.
"I'll say what we have said consistently. America's position both privately and publicly is the same. This was an outrageous act, an unacceptable murder. Those who were responsible will be held accountable by the United States of America. We're determined to do that," he said.
Khashoggi was a Washington Post columnist and Saudi dissident who was critical of the Saudi royal family in his writings and was attacked by a hit team at the Saudi consulate in Istambul, who suffocated him, tortured him and then dismembered his body with a bone saw.
Saudi Arabia had initially said Khashoggi left the consulate unharmed, but later confirmed he was killed, while denying any involvement by the crown prince.
During the first day of court hearings in the case Khashoggi's death, the public prosecutor announced Saudi Arabia is seeking the death penalty for five of the 11 men on trial.
Saudi Arabia has said it will handle the prosecution of those involved in the case and will not extradite anyone.
Pompeo said after discussing Khashoggi, he and the crown prince would talk about "all the important things we do with the Kingdom of Saudi Arabia and all the support they provide to keep Americans in Kansas and Colorado and California and in Washington, D.C. safe."
"The U.S. actions from my perspective is that it is going to further complicate, rather find any solutions to it and further entrench not only the Iranians, but also the Russians and Bashar al Assad, so from the perspective it is a very negative development," he said.
In his appearance on Face the Nation, Pompeo stated the withdrawal wouldn't diminish the United States' impact in Syria as the country can "project military power from lots of places in the world."
"The absence of a couple thousand soldiers on the ground in Syria in no way materially diminishes the capacity of the United States of America and our amazing armed forces to deliver American power to accomplish our objectives anywhere in the world," he said.