Prices of bread, cooking oil and other staples have soared since President Donald Trump withdrew Washington from the 2015 nuclear deal previous year and reimposed sanctions.
In the capital's Azadi Square, President Hassan Rouhani dismissed USA efforts to isolate Tehran while touting his country's military might.
"Islamic Iran has reached a level... to protect its borders by effective military capabilities, and firmly punish any aggressor", said Brigadier General Ramezan Sharif, spokesman for the IRGC.
State TV showed a cartoon of the Shah being thrown into the "dustbin of history", wearing clothes in US colours and holding Iranian newspapers headlined "The Shah has left!"
"After 40 years, the Islamic Republic of Iran has failed to fulfill its promises to uphold and safeguard the rights of its citizens", Bolton tweeted Monday morning.
Israel and Iran traded threats of mutual destruction on Monday as the Islamic Republic celebrated the 40th anniversary of its revolution.
The Iranian people "will not stop saying "Death to America" as long as the USA acts malicious" toward Iran, Khamenei said, referring to Trump's State of the Union address in which the American president, among other things, said: "We will not avert our eyes from a regime that chants death to America".
He also blasted a USA "conspiracy" against the country, saying, "The presence of people today on the streets all over Islamic Iran. means that the enemy will never reach its evil objectives".
Life-size replicas of Iranian-made cruise and ballistic missiles lined the route in a statement of defiance at a time of heightened tensions with the United States. "The enemies are now confessing to their defeat", said Rouhani.
Rohani Blasts U.S. 'Conspiracy' As Iran Marks 40th Anniversary Of Revolution
In Iran, the Islamic Revolutionary Guards Corps (IRGC) is the branch of the military responsible for upholding the 1979 Islamic Revolution.
In the tweets Trump said: '40 years of corruption.
"The United States does not have the courage to fire a single bullet at us despite all its defensive and military assets".
"The Iranian people have and will have some economic difficulties [due to the sanctions] but we will overcome the problems by helping each other", Rouhani said in his address.
Israeli Prime Minister Benjamin Netanyahu warned Iran that this year could be the last time it celebrates the anniversary if it attacks his country.
"If this regime makes the bad mistake and tries to destroy Tel Aviv or Haifa, it won't be successful and it will be the last anniversary of their revolution they will ever celebrate".
"They should take that into account", he said. "I am not ignoring the threats of the Iranian regime, but nor I am impressed by them", he said.
Citing leaked Iranian Judiciary documents, the Paris-based media watchdog also said that the authorities had arrested, imprisoned, or executed at least 860 journalists in the three decades between the 1979 revolution and 2009.
Today, the United States, its Arab allies and Israel are trying to counter Tehran's growing influence in the Middle East, where it has proxies in Syria, Lebanon and Yemen.
Yadollah Javani is the Revolutionary Guards' assistant head for political affairs.
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