The top US diplomat, whose visit follows his first trip to sub-Saharan Africa, will hold talks with King Salman and his son Crown Prince Mohammed bin Salman as well as Foreign Minister Faisal bin Farhan, State Department officials said.
"We'll spend a lot of time talking about the security issues with the threat from the Islamic Republic of Iran in particular," Pompeo told reporters in the Ethiopian capital Addis Ababa before heading to Riyadh.
Pompeo said the United States was "prepared to talk anytime" to Iran but emphasised that the Iranian regime has "got to fundamentally change their behaviour".
"The pressure campaign continues. It's not just an economic pressure campaign, its diplomatic pressures, isolation through diplomacy as well," he said.
US President Donald Trump, who is closely allied with Saudi Arabia, in 2018 withdrew from a nuclear accord with Iran and imposed sweeping sanctions aimed at reducing Tehran's regional clout.
Pompeo's three-day visit to close ally Saudi Arabia comes in the wake of a US-ordered drone strike that killed Qasem Soleimani, Iran's most powerful general, as he visited Baghdad on January 3.
Regional tensions rose following the killing and Iran responded with missile strikes on US forces in Iraq.
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US officials blamed Iran for a September attack on Saudi oil installations, although Riyadh has since appeared keen to engage in cautious diplomacy to ease friction.
Pompeo, who is also expected to meet deputy defence minister Prince Khalid bin Salman, faces a tough balancing act in Saudi Arabia as he said he would also discuss "human rights" alongside economic issues during his visit.
The 2018 murder of Saudi journalist Jamal Khashoggi, which sparked global condemnation of the crown prince, has tested relations between the two allies.
Five US senators have urged Pompeo to press Saudi Arabia for a resolution of a case against dual US-Saudi national Walid Fitaihi, a Harvard-trained doctor who was allegedly tortured and detained without charge for nearly two years, and end a travel ban on his family.
"It has been a consistent priority of the United States - throughout Democratic and Republican administrations - to free Americans abroad from unjust detention," the senators wrote in a letter to Pompeo.
After Riyadh, Pompeo will fly to Oman to meet the new sultan, Haitham bin Tariq, on Friday.
Pompeo will offer condolences over the death of his predecessor Qaboos, who was the Arab world's longest-serving leader and served as a go-between for Iran and the United States.
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