Secretary of State Mike Pompeo and Treasury Secretary Steven Mnuchin refused any exemption requests, insisting the US wants to maintain “unprecedented” pressure on Tehran.
After ripping up American participation in the 2015 Iran nuclear deal, Donald Trump ordered sections to be imposed on Tehran.
A number of major European companies have business with Iran but have been forced to lower their involvement in Tehran in order not to risk business prospects with the US.
French carmaker Peugeot and oil and gas firm Total are both cutting back their activities in the country.
Last month, ministers from the UK, France and Germany penned a letter to Mr Pompeo and Mr Mnuchin asking for the original nuclear deal being preserved was the “best basis on which to engage Iran” and address Mr Trump’s concerns.
The Trump administration has said there are more than 50 foreign companies that have withdrawn their business from Iran since Mr Trump announced the US was withdrawing from the 2015 nuclear deal between Iran and the United States, Germany, France, Britain, China and Russia.
Washington’s pressing other countries to stop importing Iranian crude oil and urged Saudi Arabia to increase its exports to cover the loss and prevent major disruption.
Despite protests, the Americans have signalled they have no intention of rowing back on the sanctions.
According to a letter by Mr Pompeo and Mr Mnuchin, the US ants to use sanctions to create “unprecedented financial pressure on Iran”.
Washington intends to maintain sanctions on Iran until it sees a “tangible, demonstrable and sustained shift in the policies we have enumerated”.
The US officials said: “We will seek to provide unprecedented financial pressure on the Iranian regime.”
They noted that they are “not in a position to make exceptions to this policy except in very specific circumstances”.
While holding a tough stance on exemptions, all is not lost for countries hoping for “relief”.
Mr Pompeo said: “There will be a handful of countries that come to the United States and ask for relief… We’ll consider it.”
After a hostile visit to Brussels for a meeting of Nato leaders, Mr Trump referred to the EU as a “foe” on trade issues.
EU bosses are working on a number of counter measures, including non-dollar denominated finance lines, possible direct payments for oil to Iran’s central bank, and an update to a law drawn up in the 1990s to protect European companies from previous US sanctions against Iran, Libya and Cuba.