Secretary of State Mike Pompeo Michael (Mike) Richard PompeoTreasury sanctions individuals, groups tied to Russian malign influence activities Navalny released from hospital after suspected poisoning Overnight Defense: Pentagon redirects pandemic funding to defense contractors | US planning for full Afghanistan withdrawal by May | Anti-Trump GOP group puts ads in military papers MORE ramped up his warnings to Iran on Tuesday, saying that the U.S. and its Gulf Arab allies would pay a "real high cost" for Tehran's "malign behavior" in the Middle East and elsewhere.

"One that we are most focused on today is ... that we deny Iran the financial capacity to continue this bad behavior," Pompeo told Sky News Arabia during a brief stop in the United Arab Emirates.

"So it’s a broad range, a series of sanctions aimed not at the Iranian people, but rather aimed at the single mission of convincing the Iranian regime that its malign behavior is unacceptable and has a real high cost for them," he continued.

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Pompeo also warned Tehran that "America is committed to keeping sea lines open, keeping the transit of oil available for the entire world," in a response to Iranian President Hassan Rouhani's suggestion that any disruption of Iranian oil exports could result in the disruption of oil exports throughout the region.

Tehran has threatened to block the Strait of Hormuz, a key shipping lane through which much of the world's oil passes. Pompeo said that the U.S. remained committed to ensuring that shipping lanes remained open.

"That’s the commitment we have had for decades," he said. "We continue under that commitment.”

The secretary of State's comments came as the U.S. steps up pressure on Iran after President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE's announcement in May that he would withdraw from the 2015 nuclear deal with Tehran, which sought to curb Iran's nuclear ambitions in exchange for sanctions relief.

The Trump administration has moved in recent months to impose penalties on Iranian individuals and entities, and senior U.S. officials have said that Washington has begun pressing other countries to end Iranian oil imports by November.

That push has driven up oil prices amid concerns that a divestment from Iranian oil would reduce the world's overall supply. Pompeo said that the U.S. would consider waivers for certain countries that wish to import Iranian oil, but added that Washington is determined to take a hard line on Tehran.

"We are determined to convince the Iranian leadership that this malign behavior won’t be rewarded and that the economic situation in the country will not be permitted to be rectified until such time that they become a more normal nation," he said.

— This report was updated at 10:45 a.m.