Pompeo told reporters he had also raised a number of human rights issues with King Salman and Crown Prince Mohammed bin Salman, including those of women's rights activists who have been detained for months, some allegedly tortured.
"They reiterated their commitment", Pompeo added.
Pompeo's comments on the case were some of his most stern to date, and suggested that the USA may be putting more pressure on Saudi leaders to explain what actually happened to Khashoggi, who was killed after going into the kingdom's consulate in Istanbul, Turkey in October.
The Washington Post columnist's slaying by a Saudi hit squad prompted global outrage, especially among U.S. media outlets and politicians.
"Today, the Iranian-backed Huthis have chosen not to do that".
Pompeo is due to travel to Saudi Arabia later on Sunday as part of an eight-day trip to Amman, Cairo, Manama, Abu Dhabi, Doha, Riyadh, Muscat, and finally Kuwait City.
On the detained women rights activists, Pompeo said the Saudis had committed that the "lawful judicial process would take place and they would do so quickly and that they would continue down that path". The Trump administration has been adamant that there is no established connection to Saudi's crown prince in the killing.
US Secretary of State Mike Pompeo announced on Sunday that he had signed a memorandum of understanding (MOU) with Qatar regarding the expansion and renovation of al-Udeid Air Base, which hosts thousands of US military personnel and the forward headquarters of the US military's Central Command.
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.More news: Samsung says future will 'unfold' in Galaxy S10 ad in Paris
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He also called on Qatar and other Gulf countries to end the worst political rift in the region for years, which has seen Doha diplomatically and economically isolated by neighboring former allies for the past 19 months.
Bahrain, Egypt, Saudi Arabia and the United Arab Emirates, all USA allies, began a blockade of Qatar in June 2017 that continues today.
"Disputes between countries that have a shared objective are never helpful".
Qatar - also a USA ally - denies the allegations and accuses the countries of seeking regime change.
He added that "President Trump and I both believe the ongoing dispute in the region has gone on too long".
During his tour of the Middle East, Mr Pompeo announced an global summit on the Middle East in Poland, where he will seek to unite regional actors to find a solution to Iranian aggression.
The US, 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.
For Washington, turning the page on the crisis is essential for the successful launch of the Strategic Alliance of the Middle East, a NATO-style security pact that includes Gulf countries as well as Egypt and Jordan.
Speaking during the opening session of the second US-Qatari Strategic Dialogue in Doha, Pompeo said the US and Qatar work together to settle many regional issues, including Afghanistan and Iraq.