"The regime in Tehran should understand that any attacks by them or their proxies of any identity against US interests or citizens will be answered with a swift and decisive US response," Pompeo said in a statement.
"Our restraint to this point should not be mistaken by Iran for a lack of resolve," he said.
Pompeo's statement followed the deployment of a US aircraft carrier strike group and nuclear-capable bombers to the region. Washington said in a statement it had information of plans for Iranian-backed attacks.
The escalation has raised concern in Europe, as well as among President Donald Trump's Democratic rivals, who fear the administration is pushing for war based on hyped-up intelligence.
Pompeo, however said: "We do not seek war."
"But Iran's 40 years of killing American soldiers, attacking American facilities, and taking American hostages is a constant reminder that we must defend ourselves," said Pompeo, referencing the 1979 Islamic revolution that transformed Iran from close US ally to sworn foe.
Washington reimposed crippling unilateral sanctions on Iran last year after withrawing from a landmark nuclear deal, known formally as the Joint Comprehensive Plan of Action (JCPOA).
Nuclear inspectors have long insisted that Iran has stuck by the terms of the deal, however Tehran on Wednesday said it would be suspending some of its committments to the 2015 deal.
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