US Secretary of State Mike Pompeo met with Saudi King Salman and Crown Prince Mohammad bin Salman on Monday in Riyadh, where he is visiting for talks on a range of Middle East crises, topped by the conflicts in Syria and Yemen, threats from Iran and the Saudi response to the killing of Washington Post columnist Jamal Khashoggi last year.

Riyadh is the latest stop in Pompeo's tour of the Middle East that has so far been dominated by questions and concerns about the withdrawal of US troops from Syria.

According to US officials, the major agenda items are the Saudi-led fight against Houthi rebels in Yemen and the matter of holding the perpetrators of Khashoggi's murder accountable.

Speaking with senior Saudi officials on his arrival in Riyadh late on Sunday, Pompeo stressed the importance of supporting a political solution to end Yemen's civil war and "the need for continued regional efforts to stand against the Iranian regime's malign activity and to advance peace, prosperity, and security," the State Department said.

The department said Pompeo also made clear the importance of a credible investigation into Khashoggi's killing at the Saudi Consulate in Istanbul in October. Pompeo "emphasised the importance of Saudi Arabia continuing its investigation into the murder of Jamal Khashoggi in order to ascertain facts, assess information, and hold those responsible accountable."

The relationship between Riyadh and Washington remains tense following Khashoggi's brutal slaying and dismemberment at the consulate. Members of Crown Prince Mohammed bin Salman'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.

"We will continue to have a conversation with the crown prince and the Saudis about ensuring that the accountability is full and complete with respect to the unacceptable murder of Jamal Khashoggi," Pompeo told reporters in Qatar on Sunday before heading to Riyadh.

"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."

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.

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 has long denied funding militants, but Doha shares a massive offshore natural gas field with Tehran that gives its citizens the highest per-capita income in the world.

It restored diplomatic relations with Iran after the crisis erupted, marking a setback for Saudi Arabia, which views Iran as its main regional rival.

A similar dispute involving Qatar erupted in 2014. But this time positions have hardened against Qatar, whose alleged support for opposition groups has angered the Arab nations now boycotting it.

However, comments in Doha by Pompeo and Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman Al Thani gave no sense of any movement in the ongoing diplomatic crisis with Doha.

Later, speaking to a US Embassy staff member in Qatar who said her job was moving to the UAE due to the boycott's effects, Pompeo was even more frank. "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.