One sign read, "Much to the dismay of America, the revolution has reached its 40th year".
Prices of basic foodstuffs have soared since President Donald Trump withdrew Washington from world powers' 2015 nuclear deal with Iran previous year and reimposed sanctions on Tehran.
Mr Bolton said Washington would support "the will of the Iranian people, & stand behind them to ensure their voices are heard".
"I also want to share with you that the world has been in awe of Iran's military power and its capabilities over the last 40 years and especially in the last five years..."
"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. As The Times of Israel notes, "t$3 op political and military leaders in Iran regularly call for Israel's annihilation", so Javani's paean to his regime's genocidal ambitions is not at all unprecedented.
An Iranian man marches with a portrait of the country's Supreme Leader Ali Khamenei (L) alongside a woman holding up another of Islamic Revolution founder Ayatollah Ruhollah Khomeini (R) during a ceremony celebrating the 40th anniversary of Islamic Revolution in the capital Tehran on February 11, 2019.
He also blasted a US "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".
Washington alleges Iran's launches defy a U.N. Security Council resolution calling on Iran to undertake no activity related to ballistic missiles capable of delivering nuclear weapons.
But he remained defiant on Monday as Iranians recalled the end of a monarch who catered to the rich.
A majority of Iranians blame domestic mismanagement and corruption over foreign sanctions for the economic situation, according to an IranPoll survey published in December 2018.
In January, President Hassan Rouhani said Iran was facing its worst economic crisis since the Shah was toppled.
"The United States does not have the courage to shoot a single bullet at us despite all its defensive and military assets".
"The US should know that we would raze Tel Aviv and Haifa to the ground in the event of a military attack on us", General Yadollah Javani, head of the guard's political bureau, was quoted as saying.
Israeli Prime Minister Benjamin Netanyahu was quick to respond saying later on Monday it would mark Iran's last revolution anniversary if it attacked any cities in Israel. "They would do well to take that into account".
The cry of "Death to America" has long featured in the Islamic republic, with leaders and the public alike using it to vent their perception of America's supposed interest in working against the country.
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.