The commander's statement comes after earlier in the day the IRNA cited an Iranian Islamic Revolutionary Guard Corps (IRGC) spokesman who stated that Tehran's military forces will "firmly punish" aggressors who attack Iran.
Tehran's downtown Enghelab, or Revolution Street, is decorated with huge balloons.
And he vowed to overcome US efforts to isolate Tehran.
Speaking from a podium in central Tehran, Iranian President Hassan Rouhani addressed the crowds for almost 45 minutes, lashing out at Iran's enemies - America and Israel - and claiming their efforts to "bring down" Iranians through sanctions will not succeed.
Tensions between Washington and Tehran are high after the U.S. withdrew from an global nuclear deal aimed at curbing Iran's nuclear ambitions, and re-imposed sanctions that have hurt the Iranian economy.
The Ayatollah urged crowds to turn out in vast numbers for the 40th anniversary of the revolution in a show of Iranian unity to the world.
President Donald Trump slammed Iran's Islamic revolution as a complete failure for the country in tweets written in both English and Farsi Monday on the 40th anniversary of the Iranian Revolution.
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Rouhani lambasted calls from the United States and Europe for a fresh agreement to curb Iran's missile program. Tehran denies the charge, insisting its satellite launches and rocket tests do not have a military component. "The regime in Iran has produced only #40YearsofFailure", he wrote.
Rouhani also promised that Iran would overcome its economic hardships, worsened by the restored USA sanctions.
State television offered blanket coverage of the commemorations, showing marches in cities ranging from Abadan in southwestern Iran to Mashhad in the northeast. "I see a bright future for him and our nation", Hosseinpour said.
Fakheri, who was one of the revolutionaries on the streets of Tehran in 1979, said she would defend the revolution all over again. "I don't think you'll have many more anniversaries to enjoy".
Imam Khomeini had lived many years in exile, in Iraq and France, before returning home and leading a historical revolution that overthrew Pahlavi regime.
In January, Rouhani said Iran was dealing with its worst economic crisis since the Shah was toppled.
"I bow in admiration to Iran's resilient people who - despite hardships and grievances - today poured into streets by the millions to mark 40th anniversary of their Islamic Revolution, which some in the U.S. wished would never come", Iranian Foreign Minister Mohammad Javad Zarif tweeted.