The outpouring of anti-US sentiment came despite a landmark nuclear deal between Iran and major powers including Washington in July.
The storming of the embassy by students, months after the Islamic revolution, led to a 444-day hostage crisis and a break in diplomatic relations that continues to this day.
Demonstrators gathered outside the former US embassy in Tehran and across Iran for what was declared "national day of the fight against global arrogance" -- a term often used by supreme leader Ayatollah Ali Khamenei.
Protesters held placards with slogans including "Down with U.S.A" and "Down with Israel".
Prosecutor General Ebrahim Raisi gave a fiery speech attacking US "atrocities" ranging from slavery, the treatment of Native Americans, phone tapping and "the killing of 300,000 Iraqis".
"A day will come when they will have to answer in court for their atrocities," he said.
On Monday, a majority of Iranian legislators said the Islamic republic would not drop the "Death to America" slogan despite the nuclear accord.
Khamenei has endorsed the July 14 deal which curbs Iran's atomic drive in return for a lifting of sanctions, but has repeatedly warned against US "infiltration" of the values of Iranian society.
Personal note: I think Raisi is right that one day the United States of America will have to answer for what we did to our Native Americans and for slavery, but phone tapping is not even close to that level of damnation. However, there is not much difference in a foreign power killing citizens of a another country and that other country killing their own citizens because they refuse to help them out of poverty... killing is killing, when one gets down to it. But, I do think that it is time for the United States of America to pull out of that area of the Middle East and let those people sink or swim by their own hand, up until that point when they become a threat to OUR way of life, then we should swat them down like a stink bug.