The leaders spoke at a rally marking 40 years since the Islamic revolution, a political natural disaster that ended millennia of monarchy and still reverberates around the region.
This year's anniversary comes as tensions rise with the United States and Iran grapples with the aftermath of President Donald Trump's pullout last May from the 2015 nuclear deal between Iran and world powers and tough US economic sanctions, re-imposed in November.
Ballistic missile capabilities were on display during the main march, including the Qadr F, a ground-to-ground missile with a 1,950-km (1,220-mile) range, Tasnim news agency said.
President Hassan Rouhani told a crowd in Tehran that Iran's enemies will not achieve what he called their evil goals.
The 10-day period from the return of Imam Khomeini until the revolution's victory is celebrated annually in Iran, and is known as the Ten-Day Fajr (Dawn).
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.
"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.
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".
"US should take note: REAL Iranians never succumb to diktats".
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"The presence of people in this celebration means that plots by the enemies ... have been defused", Rouhani said. Iranian people have and will have some economic difficulties but we will overcome the problems by helping each other, ' Rouhani said.
Iranians march towards Azadi Square during Monday's rally.
"The United States does not have the courage to fire 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 has responded to the IRGC's harsh rhetoric about attacking Israel on Monday, saying that although he was "not ignoring the threat of the Iranian regime", he was also "unimpressed by them".
"Were this regime to make the awful mistake of trying to destroy Tel Aviv and Haifa, it would not succeed, but it would mean that they had celebrated their last Revolution Day".
Washington and the Arab world have viewed Iran with great suspicion since the Islamic Revolution, fearing Khomeini's radical ideology would inspire militants across the Middle East.
Today, Iran enjoys influence through proxies in Iraq, Syria, Lebanon and Yemen, raising concerns in Sunni Saudi Arabia, which accuses its rival of trying to dominate the Middle East. Tehran denies the allegations.