Donald Trump threatened to attack Iran in retaliation for any strikes by Tehran "on anything American".
The threat came after Iran said new US sanctions precluded any diplomacy and called the White House actions "mentally retarded."
"Iran's very ignorant and insulting statement, put out today, only shows that they do not understand reality.
"Any attack by Iran on anything American will be met with great and overwhelming force. In some areas, overwhelming will mean obliteration," Trump said in a Twitter post.
With tensions running high between the two countries, Trump signed an executive order imposing the sanctions, which Treasury Secretary Steven Mnuchin said would lock billions of dollars more in Iranian assets.
Trump said the new sanctions were in part a response to last week's downing of a US drone, but would have happened anyway.
He said the supreme leader was ultimately responsible for what Trump called "the hostile conduct of the regime."
Trump said Friday that the US was prepared to carry out a retaliatory strike, but that he called it off after learning at the last minute of the expected Iranian casualties.
The president has in recent weeks adopted alternating rhetoric toward Iran, at times threatening an aggressive military response if provoked and at other times expressing a desire to negotiate with Tehran.
"I think a lot of restraint has been shown by us, a lot of restraint, and that doesn’t mean we’re going to show it in the future,” the president said Monday.
