Iranian supreme leader Ayatollah Ali Khamenei's top military aide also threatened to shower Saudi royal palaces "with 1,000 missiles" if the kingdom launches an attack.
The Iranian military's chief of staff said America "is a disloyal, atrocious, criminal, isolated, angry enemy with disloyal, corrupt leaders."
Speaking at a military showcase, President Rouhani blamed "invading powers" for shoring up presence around Iran.
Iranian Foreign Minister Mohammad Javad Zarif said, "It was the people who made the Islamic Republic of Iran so powerful."
Iranian Major General Qassem Soleimani, commander of the Islamic Revolutionary Guard Corps' Quds Force, has left the shadows for the spotlight.
"Those who have to leave Syria are the ones who have not been permitted by the Syrian government," said one of the top advisers to Iran's supreme leader.
Iran is looking to project its military power and establish ties abroad at a time when the U.S., Israel and Saudi Arabia have tried to isolate it.
The Pentagon is conducting a major review as Iran announces the U.S. military has been added to a list of groups threatening regional stability.
Turkey and Iran, traditional foes, have established common ground in Iraq, Syria and Qatar as regional alliances shift.
Military leaders said they did not fear an invasion from the West, touting Tehran's growing military might at home and abroad.
"The Americans will take this dream to their graves," a senior adviser to Ayatollah Ali Khamenei said,
Former U.S. and Israeli generals disavow a possible U.S. military strike on Iran, and a European scholar says Trump may find himself isolated.
Majority-Shiite Muslim neighbors Iran and Iraq have a volatile history and differing views on the U.S., but they share an interest in battling jihadis.
The three countries all want a stake in Syria's future and appear willing to secure it by making long-term military commitments.
More than 64 years after the CIA helped overthrow Iran's democratically elected government, the country reacted to recent U.S. comments on regime change.
The U.S. chopper reportedly triggered its automatic defense system, setting off flares.