The hostage-taking - brought to Americans' living rooms for 444 days in one of the first global crises televised in near real-time - still haunts relations between the two former allies which have never re-established diplomatic relations.
Secretary of State Mike Pompeo pointed to the embassy siege as the United States announced sanctions against nine aides to Ayatollah Ali Khamenei, Iran's supreme leader under the Islamic republic established by the revolution.
"Forty years later, the revolutionary regime in Tehran has proven, time and again, that its first acts after gaining power were a clear indication of its evil character," Secretary of State Mike Pompeo said in a statement.
The Treasury Department said it was imposing the sanctions - which criminalize financial transactions by anyone in the United States - over "repression" at home and the export of "terrorism" overseas.
The targeted individuals include a number of prominent Iranians, among them judiciary chief Ebrahim Raisi and Ali Akbar Velayati, a senior foreign policy advisor to Khamenei.
Velayati, who served as Iran's foreign minister from 1981-1997, is wanted in Argentina in connection with the 1994 bombing of a Jewish center blamed on Hezbollah, the Lebanese Shiite militant group with close ties to Tehran. The United States said it was also offering a $20 million reward for information to find Robert Levinson, a former FBI agent and CIA contractor who went missing in Iran in 2007 in mysterious circumstances.
In a speech, the head of the army, General Abdolrahim Mousavi, denounced the idea of interaction with the United States as a ruse - echoing recent remarks by Khamenei after Trump said he was open to dialogue. "They will continue their enmity against us. They are like a lethal scorpion whose nature is to have a poisonous sting," Mousavi said.
"We are ready to crush this scorpion and will also pay the price," he said.
Trump withdrew last year from a nuclear accord negotiated by his predecessor Barack Obama that had raised the possibility of US reconciliation with a country where most of the population was born after 1979.
Trump instead slapped sweeping sanctions, including trying to end all Iranian oil exports.
Iran on Monday announced its latest action meant to defy but not kill the 2015 nuclear agreement, which is still backed by European powers.
Iran has increased enriched uranium production to 11 pounds (five kilograms) a day, more than tenfold the amount from two months ago, and has developed two new advanced centrifuges, said Ali Akbar Salehi, the head of the Atomic Energy Organisation of Iran.
Outside the former embassy turned museum, replica missiles and the same type of air defense battery used to shoot down a US drone in June were put on display. Iranians massed in front of the building carrying placards with slogans such as "Down with USA" and "Death to America." "We will sacrifice our lives and existence for the leader and this system, and we will not be intimated by our enemy, which is America," Sajad Shirazi, a stonecutter, told AFP at the rally.
State TV aired segments of a Canadian documentary titled "The Fire Breather" showing Trump's controversial 2016 campaign trail highlights and biting comments about his past alongside images of the rallies.
"Americans, at the time (of the embassy takeover) believed they were an exceptional nation, able to commit any injustice anywhere," government spokesman Ali Rabiei told the press on Monday. "America's problem is still this sense of exceptionalism. It allows itself to trample international law and commit the worst crimes against nations with no fear of an international backlash," he added.
Revolutionary students described the embassy as a den of spies who plotted with the shah, the monarch who oriented the ancient nation toward the West but clamped down on dissent at home.
Gary Sick, who handled the hostage crisis at the National Security Council under then president Jimmy Carter, said the episode had scarred the US psyche and explained Washington's hawkish stance. "If you look at everything Iran has done or we have done in the meantime, the kind of punishment that is being meted out to Iran is totally disproportionate," he said. But Sick, a professor at Columbia University, said that the reaction served as a lesson for any nation tempted to support such a flagrant breach of diplomatic protocol. "Any country that is tempted to do something like this will look back at the price that Iran has paid and see it is not worth it, not just in terms of money but in reputation," he said.