"But if they attack us, we will raze Tel Aviv and Haifa to the ground", Yadollah Javani, the Guards' deputy head for political affairs said during a rally celebrating the 40th anniversary of the Islamic revolution.
Some of the protesters burned USA flags.
Every year, the anniversary festivities start on February 1 - the day Khomeini returned home from France after 14 years in exile to become the supreme leader as Shiite clerics took power - and continue for 10 days, climaxing on February 11.
On Feb 11, 1979, Iran's army declared its neutrality, paving the way for the collapse of the Shah Mohammad Reza Pahlavi, the United States's closest ally in the Middle East.
Iranians celebrated the 1979 overthrow of Shah Mohammad Reza Pahlavi, who was supported by the USA, "waving Iranian flags, chanting "Death to America" and burning US and Israeli flags", reported The Associated Press.
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.
"40 Years of Failure to accept that Iranians will never return to submission".
Soldiers, students, clergymen and women wearing black filled streets across Iran.
The Jerusalem Post reports that Monday's demonstrations featured hundreds of thousands of Iranian citizens - "s$3 oldiers, students, clerics and black-clad women holding small children" alike - and that some burned USA flags.
The large turnout in state-sponsored rallies came as Iranians face rising prices, food shortages and high inflation that have triggered waves of protests.
Life-size replicas of Iranian-made cruise and ballistic missiles stood in a statement of defiance after the US past year reimposed sanctions following its withdrawal from a deal on Tehran's nuclear programme.
He compared the US sanctions and economic hardships to "riding a bicycle when someone puts a stick in the wheels" but pointed to advances in other fields as more than making up for them.
In January, President Hassan Rouhani said his country was experiencing its worst economic crisis since the overthrow of the Shah. Iran insists that it has the right to operate in Syria, since it has been invited by Assad to help rebuild the country.
In a speech at Tehran's Azadi (Freedom) square, Rouhani said US efforts to isolate Iran would fail.
Rouhani also promised the crowds that Iran would overcome the economic hardship amid the country's spiraling economy and the newly imposed USA sanctions. He said, "The United States does not have the courage to shoot a single bullet at us".
The latest such assault took place on Monday evening, with Syria's state news agency SANA reporting that Israeli artillery targeted a number of sites in Quneitra province.
"I said that they won't succeed and if they try it will be the last anniversary they celebrate", he said.
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