The annual state-organised rally drew greater attention this year, as Iranian hard-liners look to counter moderate President Hassan Rouhani's outreach to the West following a landmark nuclear deal reached with world powers in July.
An Iranian official also chose the occasion to announce the arrest of an unspecified number of allegedly pro-American writers.
The hard-liners fear Rouhani's efforts to improve relations will pave the way for the United States to undermine and eventually dismantle the Islamic republic formed after the 1979 revolution.
The students held the hostages for 444 days, and the two countries have had no diplomatic relations since then.
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Protesters today carried placards reading "political and security penetration is forbidden." They pumped their fists in the air, shouting "God damn America," and "No compromise, no surrender to US"
Others carried banners rejecting US fast food chains McDonald's and Starbucks. Authorities recently closed a newly opened knock-off of KFC, saying it was unlicensed.
Foreign firms are poised to return to Iran following the lifting of international sanctions under the nuclear deal, but it remains unclear whether American brands will be allowed in.
Iran's state TV showed similar demonstrations in other Iranian cities to mark the occasion, known as the "National Day against Global Arrogance."
Today's rally in Tehran also saw State Prosecutor Ebrahim Raeisi announce that the intelligence department of the elite Revolutionary Guard had detained a number of writers.
"Under no circumstances will we allow penetration of Americans in economic, social and cultural areas," he added.
Iran has arrested a number of activists, journalists and artists since Rouhani's 2013 election and currently holds four Iranians with US citizenship, including a Washington Post reporter. Analysts say the arrests are the work of hard-liners in the judiciary and the security forces.