A Central Intelligence Agency assessment has blamed Prince Mohammed for ordering the killing of Khashoggi, a longtime royal insider who had become a critic of the crown prince, inside the Saudi consulate in Istanbul on October 2.
"We'll continue to talk about that and make sure we have all the facts so that they are held accountable certainly by the Saudis, but by the United States as well, where appropriate", he added.
Qatar's Deputy Prime Minister and Minister of Foreign Affairs H E Sheikh Mohammed bin Abdulrahman al-Thani also said his country's relationship with America "has enabled us to confront so many regional and worldwide challenges".
The trip was cut short after Pompeo met with the Saudi king and crown prince in what is the latest stop of his Middle East tour that has so far been dominated by questions and concerns about the withdrawal of U.S. troops from Syria.
On a previous visit to Riyadh at the height of the Khashoggi affair, Pompeo's broad smiles with the crown prince outraged some Americans. Members of Crown Prince Mohammed bin Salman's entourage have been implicated in the killing and USA lawmakers have demanded America pull back its support of the Saudi-led war in Yemen.
Saudi officials have denied accusations that the prince ordered the murder, which has left the kingdom facing its worst political crisis in generations, strained ties with Western allies and focused attention on the prince's domestic crackdown on dissent and the war in Yemen.
Rights groups have called on Pompeo to also press Prince Mohammed over the jailing of women activists in the kingdom, amid claims that many of them faced sexual harassment and torture during interrogation.
During his visit to Qatar, Pompeo refused to comment on reports Washington had recently considered military action against Tehran.
Bahrain, Egypt, Saudi Arabia and the United Arab Emirates began a boycott of Qatar in June 2017, alleging Qatar funds militant groups and has too-cosy ties with Iran.
Qatar - also a USA ally - denies the allegations and accuses the countries of seeking regime change.
"We're all more powerful when we're working together", Pompeo said at a news conference.
"It's on everyone's mind and not at all clear that the rift is any closer to being resolved today than it was yesterday - and I regret that", Pompeo said.
Pompeo later told reporters that he had also raised the rift with officials in Bahrain, Egypt and the UAE.
Speaking with senior Saudi officials on his arrival in Riyadh late Sunday, Pompeo stressed the importance of ending fighting in Yemen and keeping up pressure Iran.
The United States, which at first appeared to back the boycott of Qatar, has so far been unsuccessful in trying to end the dispute.
Mediation efforts by the United States, which at first appeared to back the boycott of Qatar, have stalled, as highlighted by the recent resignation of U.S. envoy Anthony Zinni.
"It was time for change and he made his decision to move on but America's commitment remains unchanged", said Pompeo of Zinni.