The US embassy was stormed in 1979 by radical students who held dozens of diplomats hostage for 444 days.
Demonstrators burnt US and Israeli flags as well as effigies of Uncle Sam and George Bush, the US president, outside the former embassy on Saturday.
Student protesters carried banners proclaiming "death to America", "death to Israel" and "America is the Great Satan".
Mohsen Abdullahi, a student, said: "We are here to punch America in the mouth. We want to tell the Americans and British they are nothing in the face of Iran's power."
Many high school students had been let out of class to attend the annual demonstration and while the crowd appeared to number up to 10,000, turnout was not as big as in previous years.
Amir Hossein Ebrahimi, a 14-year-old student who wore camouflage fatigues, said: "I wore this to tell the Americans that Iranians are always ready to join the army and defend our country."
'Learned its lesson'
Gholamali Haddadadel, the parliamentary speaker, told protesters: "Unfortunately, America has not learned its lesson from the takeover of its embassy, they should know that threats and sanctions do not affect the will of this great nation."
The crowd shouted: "Nuclear energy is our certain right."
Pressing home that message, Iran on Thursday started 10 days of military exercises off its southern coast and said it had test fired new and improved missiles. Tehran says all the Gulf's vital oil shipping lanes are now within range of its weaponry.
Iran's Revolutionary Guards tested a new generation of anti-tank, anti-helicopter and anti-personnel weaponry during Saturday's manoeuvres.
The semi-official Fars news agency quoted brigadier-general Mohammad Reza Zahedi, the Guards' land forces commander, as saying: "By relying on God, the Revolutionary Guards will use different types of modern equipment and advanced tactics to destroy the enemies' advanced systems.
"We hope the enemies have no ominous intentions and will not repeat their past experiences."