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.
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 faces a tough balancing act in Saudi Arabia as he said he would also discuss "human rights" 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.
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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