© Atta Kenare (AFP)Iranian women walk past the former US embassy in Tehran on November 3, 2016, during a demonstration marking the start of its 1979 siege.
"America is no longer number one and the first power of the world," deputy Revolutionary Guards commander Hossein Salami told thousands gathered outside the former US mission in Tehran.
"America's political will can no longer manage political and military development in... the world of Islam. America's political power has strongly declined."
During the 444-day siege of Tehran's US embassy, more than 50 diplomats, staff and spies were taken hostage.
The crisis severed US-Iranian diplomatic ties for decades, but Tehran last year clinched a deal with world powers to curb its controversial nuclear program in exchange for an easing of economic sanctions.
Protesters on Thursday chanted the traditional rallying cries of "Death to America" and "Death to the House of Saud", in reference to Iran's regional rival Saudi Arabia.
But the US remains Iran's main enemy, and Tehran and Washington back opposing sides in several regional conflicts, including Syria and Yemen.
"Our fight with the Americans will continue" Salami said. "Pursuing our ideals in the world of Islam and in Iran, we will recognize no stopping point or red line.
He also warned the US not to criticize Iran's ballistic missiles, calling its system "the real center of our power (that) must be strengthened."
© Atta Kenare (AFP)An Iranian youth burns home-made American flag outside the former US embassy Tehran on November 3, 2016.
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