His comments came hours after the Trump administration restored all sanctions lifted under the 2015 nuclear deal, targeting core parts of Iran's economy.
Iran's President Hassan Rouhani earlier struck a defiant tone, saying the country will "continue selling oil".
"We will proudly break the sanctions," he told economic officials.
Mr Pompeo told reporters: "The Iranian regime has a choice: it can either do a 180-degree turn from its outlaw course of action and act like a normal country, or it can see its economy crumble."
He said more than 20 nations had already cut their oil intake from the Islamic Republic, and its exports had fallen by a million barrels a day.
European countries which are still party to the 2015 accord have said they will help businesses bypass the sanctions. But there are doubts about how successful this will be.