"We'll be talking with them about how to make sure that we are all strategically aligned and how we can build out a global coalition" on Iran, he said.
Iran shot down a US Global Hawk drone on Thursday, saying it had violated its airspace near the strategic Strait of Hormuz -- a claim the United States denies.
US President Donald Trump called off a planned retaliatory military strike Friday, saying the response would not have been "proportionate," with Tehran warning any attack would see Washington's interests across the Middle East go up in flames.
Pompeo said he would stop in the two countries on his way to India, where he begins a visit on Tuesday.
Speaking to reporters as he left Washington, Pompeo called Saudi Arabia and United Arab Emirates "great allies in the challenge that Iran presents."
Pompeo denounced a map that was released by Iranian Foreign Minister Mohammad Javad Zarif that purported to show a spy drone encroaching its airspace in late May and urged media not to find it credible.
"You've seen that child-like map that Foreign Minister Zarif put out that contrasts with the excellence and professionalism of America's military and intelligence services," Pompeo said.
Pompeo said that Iran's map "should leave no doubt in anyone's mind about where that unarmed vehicle was -- it was flying in international airspace."
"We shouldn't let the Iranians have one moment where any reporter would write that there is even a credible response to the data set that the Americans have put forward," he said, accusing Iran of "sowing disinformation in lots of lots of places."
But Pompeo reiterated Trump's offer of dialogue to improve relations with Iran, which the US administration has sought to isolate through harsh sanctions.
"We're prepared to negotiate with no preconditions. They know precisely how to find us," Pompeo said.
"And I am confident that at the very moment they're ready to truly engage with us, we will able to begin this conversation," he said.
"I'm looking forward to the day," he added.
