The crowd chanted "Down with US" and "Death to Israel" during Sunday's rally in the capital, and state TV says similar demonstrations were held in other cities and towns.
Asked if the USA had assurances from India and China - suspected to be among the nations getting waivers - that they would eventually give up importing oil from Iran, Pompeo wouldn't say.
The US stance has already inflicted serious pain on Iranians, with the country's currency, the rial, losing more than two thirds of its value since May. The head of Iran's powerful Revolutionary Guard warned America that it would threaten Iran at its own peril.
The UK, Germany and France - which are among the five countries still committed to the nuclear pact - have all objected to the sanctions, the BBC said.
"US bullying is backfiring".
Later a senior State Department official told reporters that the U.S. was ready for talks with Iran. In his presidential statement, Trump called on the regime to abandon its nuclear ambitions, change its "destructive behaviour", respect the rights of its people, and return in good faith to the negotiating table.
British business leaders demand ‘people’s vote’ on Brexit deal
Lord Bilimoria responded: "I don't think they would, they've had a shock". And there is not great support for a second referendum in parliament.
The other parties to the nuclear deal - Britain, France, Germany, China and Russian Federation - have all vehemently opposed the United States move and vowed to keep trade going, though they are struggling to convince private companies to stand up to USA pressure.
Rouhani separately said leaders from "four powers" met with Iran on the sidelines of the September meeting of the United Nations General Assembly to try to save the deal, including brokering a possible meeting with Trump. For now, Iran continues to abide by the accord which saw it limit its enrichment of uranium.
News of the waivers initially helped lower oil prices early on Monday, since they allow major buyers to import Iran's oil for a while. But Brent crude was steady at $72.83 by 1230 GMT. US light crude was 15 cents lower at $62.99.
Pompeo responded by saying that no one would call either himself or President Trump soft on Iran.
Days ahead of the U.S.'s important midterm elections, Donald Trump has continued on his crusade to stoke fear in the hearts of America's conservatives with blatant lies and racism. Campaigning in Chattanooga, Tennessee, on Sunday, Trump said his "maximum pressure" against Iran was working.
On "Face the Nation" Pompeo confirmed that "European countries will not be permitted to do business with both the United States and with Iran".