"The United States does not have the courage to shoot a single bullet at us despite all its defensive and military assets. But if they attack us, we will raze Tel Aviv and Haifa to the ground," Yadollah Javani, the Guards' deputy head for political affairs was quoted as saying by state news agency IRNA.
He was speaking at a rally celebrating the 40th anniversary of the Islamic revolution.
Hundreds of thousands of Iranians marched and some burned U.S. and Israeli flags on Monday to mark the 40th anniversary of the triumph of Ayatollah Ruhollah Khomeini, the Shi'ite cleric who toppled the Shah in an Islamic Revolution that rattles the West to this day.
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On Feb 11, 1979, Iran's army declared its neutrality, paving the way for the fall of Shah Mohammad Reza Pahlavi, the United States' closest ally in the Middle East.
State TV showed crowds defying cold rainy weather and carrying Iranian flags while shouting "Death to Israel, Death to America," trademark chants of the revolution which ousted the United States' most important ally in the Middle East.
"Much to the dismay of America, the revolution has reached its 40th year," read one banner.
Marchers carried cardboard cutouts of dogs. One had the face of Trump and the other the face of Israeli Prime Minister Benjamin Netanyahu.
State TV showed a cartoon of the Shah being thrown into the "dustbin of history", wearing clothes in U.S. colors and holding Iranian newspapers headlined "The Shah has left!"