They however adhered to agreements made in December at talks in Sweden to end nearly four-year civil war between Yemen's Saudi-backed government and the Iranian-aligned Houthis.
Pompeo has said he would also discuss the investigation into the murder of Saudi journalist Jamal Khashoggi inside the Saudi consulate in Istanbul in October, but no details of that discussion were immediately available.
After evidence emerged that the killing was done by a team of Saudis sent from Riyadh and closely linked to Crown Prince Mohammed bin Salman, the global community demanded a transparent investigation.
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.
"This curtailment of travel is required so that the Pompeo family may attend a family funeral", the spokesman said.
At each stop, Pompeo has sought to reassure Arab leaders that President Donald Trump's decision to withdraw US forces from Syria does not mean Washington is abandoning the Middle East or the fight against the Islamic State group.
He said the Saudis reiterated their pledges to pursue the case wherever it leads, but would not comment on USA intelligence suggesting the crown prince may have ordered the killing himself. He released a statement saying, "Our intelligence agencies continue to assess all information, but it could very well be that the Crown Prince had knowledge of this tragic event - maybe he did and maybe he didn't!"
He added that Khashoggi's murder is unacceptable, and he will work to get new answers from the Saudis during his visit. USA lawmakers also demanded America pull back its support of the Saudi-led war in Yemen.
The US and Qatar held the second "strategic dialogue" between the two countries on Sunday, and signed agreements on defence, education and culture.
"So, 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".
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.
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".
In mid-2017, Saudi Arabia, Egypt, the UAE and Bahrain severed diplomatic and trade ties with Qatar, accusing Doha of supporting terrorism, an accusation vehemently denied by Qatar.
The U.S. Embassy in Riyadh said that Pompeo and the crown prince had agreed on the need for a continued de-escalation in Yemen.
"(It's) not at all clear that the rift is any closer to being resolved today than it was yesterday", he said.
In Doha on Sunday, Pompeo made similar remarks, but he said that while the United States could try to play peacemaker, it is ultimately up to the countries involved to resolve the situation. But this time positions have hardened against Qatar, whose support for Islamist opposition groups has angered the Arab nations now boycotting it.
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