"I recently offered to travel to Tehran and speak directly to the Iranian people. The regime hasn’t accepted my offer," he tweeted.
He added that Washington was not afraid of Iranian officials coming to the United States.
"We aren’t afraid of @JZarif [Iranian Foreign Minister Javad Zarif] coming to America where he enjoys the right to speak freely. Are the facts of the @khamenei_ir [Supreme leader of Iran Ali Khamenei] regime so bad he cannot let me do the same thing in Tehran? What if his people heard the truth, unfiltered, unabridged?" he added.
In a separate interview broadcast by Fox News, Pompeo said that Washington had already asked Japan, France, Germany, South Korea, Australia and other nations to join a planned maritime security initiative in the Middle East.
"Every country that has an interest in ensuring that those waterways are open and crude oil and other products can flow through the Strait of Hormuz needs to participate," Pompeo said.
A senior diplomat in Japan, Washington's key Asian ally, told Reuters that Pompeo had talked with Prime Minister Shinzo Abe by telephone on Friday, but that Japan was not in a position to decide if or how it could join any maritime force until the United Sates provided a blueprint of how such an operation would work.
"We don't know where they want to lead," he said, asking not to be identified because he was not authorized to talk to the media.
Pompeo's comments came after Iran on Wednesday tested what appeared to be a medium-range ballistic missile that traveled about 1,000 km (620 miles), said a U.S. defense official, who spoke on condition of anonymity. The test did not pose a threat to shipping or any U.S. personnel in the region, the official said.