Pompeo met with Saudi King Salman and Crown Prince Mohammed bin Salman on the latest stop of his Middle East tour that has so far been dominated by questions and concerns about the withdrawal of USA troops from Syria.
The top U.S. diplomat, on an extensive Middle East tour, embarked on his second politically sensitive visit to Saudi Arabia since Khashoggi's October 2 murder inside its Istanbul consulate sparked an global outcry.
Trump has said he wants to preserve the alliance with the Saudi kingdom, although the US Senate has clearly blamed Prince Mohammed for the murder. He would not comment on USA intelligence suggesting the crown prince may have ordered the killing.
Pompeo says Khashoggi's murder is unacceptable, and he will work to get new answers from the Saudi Crown Prince during his visit..
The relationship between Riyadh and Washington remains tense following Khashoggi's brutal slaying and dismemberment at the consulate.
Pompeo stressed the importance of ending fighting in Yemen and keeping up pressure Iran. Members of Prince Mohammed's entourage have been implicated in the killing and US lawmakers have demanded America pull back its support of the Saudi-led war in Yemen.
Arriving in Riyadh, Pompeo was greeted at the airport by Adel al-Jubeir, the Saudi minister of state for foreign affairs, Prince Khalid bin Salman, the Saudi ambassador to Washington, and U.S. Charge D'Affaires Christopher Henzel.
"We will continue to work to ensure that all those responsible for the murder of Jamal Khashoggi are accountable", Pompeo said Friday on the United States channel Fox News.
U.S. Secretary of State Mike Pompeo said Sunday an ongoing boycott of Qatar by four of America's allies in the Middle East "has dragged on too long", though he gave no sign of any coming breakthrough in the dispute.
Saudi Arabia, the United Arab Emirates, Bahrain and non-Gulf Cooperation Council (GCC) member Egypt cut diplomatic, transport and trade ties with Qatar in June 2017, accusing it of supporting terrorism and their regional foe Shi'ite Muslim Iran - something Doha denies.
Qatar's Foreign Minister Sheikh Mohammed bin Abdulrahman Al Thani also said his country's relationship with America "has enabled us to confront so many regional and global challenges".
"We will continue to have a conversation with the crown prince and the Saudis about ensuring accountability", Pompeo said in Doha after talks with Qatari government officials. It restored diplomatic relations with Iran after the crisis erupted, marking a setback for Saudi Arabia, which views the Shiite power Iran as its main regional rival.
In Doha on Sunday, Pompeo made similar remarks but said that while the United States could try to play peacemaker, it is ultimately up to the countries involved to resolve the situation.
"It is complicated to put together, make no mistake about it, because we're talking about a complex agreement among a number of nations where we're asking for significant commitments from them", Pompeo told reporters in Abu Dhabi on Saturday.
"(It's) not at all clear that the rift is any closer to being resolved today than it was yesterday", he said.