By contrast, President Trump has made it clear that he is not willing to sacrifice America's trading relationship with Saudi over the death of Khashoggi, who was living and working in the United States when he was killed.
As the Trump administration struggles to clarify confusion over its Syria policy and the impending withdrawal of USA troops, the latest tweets from President Donald Trump have even his top diplomat guessing at what they might mean.
Khashoggi, a contributor to Middle East Eye and the Washington Post, was murdered by a team of 15 Saudi hitmen on 2 October, shortly after entering the kingdom's consulate in Istanbul.
Khashoggi, a long-time royal insider who had become a critic of the kingdom's Crown Prince Mohammed bin Salman, was killed inside the Saudi consulate in Istanbul on October 2.
"Where friends think the other one has fallen short, I was very clear and candid about those things where America is not satisfied with and where they are not meeting our expectations", said Pompeo.
The slow response to Khashoggi's killing, amid a torrent of intelligence leaks from Turkish authorities about Khashoggi's death and alleged torture and dismemberment, have bruised Prince Mohammed's reputation at home and overseas as a modernizing reformer in Saudi Arabia.
It took 17 days for Saudi Arabia to admit that Khashoggi, an insider-turned-critic of the regime who went into self-exile, was dead.More news: Duke Star Zion Williamson Suffers Eye Poke During Florida State Game
"We will continue to have a conversation with the crown prince and the Saudis about ensuring the accountability is full and complete with respect to the unacceptable murder of Jamal Khashoggi", Pompeo told reporters in Qatar, before flying to Riyadh.
Saudi authorities deny the torture charges, and Prince Mohammed has said they have recordings showing the activists were working with foreign intelligence agencies.
Earlier this month, the trial of 11 Saudis suspected of involvement in Khashoggi's murder opened, with the kingdom's public prosecutor saying that the death penalty has been recommended for five of them.
Pompeo will travel to Saudi Arabia after his daylong stay in Doha.
"A comprehensive political solution is only way to the end the conflict", the Embassy said.
"It diminishes our ability to all work together", he said of the spat that began in 2017 with Bahrain, Egypt, Saudi Arabia and the United Arab Emirates boycotting of Qatar, which it accused of funding extremist groups.
Qatar - also a United States ally - denies the allegations and accuses the countries of seeking regime change.
Pompeo described the two countries' relationship as "extensive, important and growing".
The ongoing dispute between Qatar and four of America's other close Arab partners will also feature in Pompeo's talks as it continues to be a major hindrance in a US -led effort to unite the Gulf Arab states, Egypt and Jordan in a military alliance to counter Iran.
However, Pompeo later admitted in a Q&A session with USA embassy staff in Doha that no progress was made on resolving the issue. "It's ... not at all clear that the rift is any closer to being resolved today than it was yesterday and I regret that", he said.