Tehran was quick to retaliate on Monday by declaring US troops "terrorists" following Washington's move, which was welcomed by Iran's regional arch-rivals Israel and Saudi Arabia.
It was the first time that Washington has branded part of a foreign government a terrorist group, meaning that anyone who deals with the Islamic Revolutionary Guard Corps could face prison in the United States.
"Who are you to label revolutionary institutions as terrorists?" an angry Rouhani demanded in a speech broadcast live by state television.
Rouhani hailed the Guards for fighting terrorism since their creation in 1979, and accused US forces of having always been involved with terrorist groups or acts of terrorism.
"You want to use terrorist groups as tools against the nations of the region... you are the leader of world terrorism.
"Who is propagating and encouraging terrorism in today's world? Who wanted to use ISIS (the Islamic State group) as a tool?" Rouhani asked, saying that the US is "hiding" the leaders of the jihadist organisation.
The Revolutionary Guards are the ideological arm of the country's military and deeply embedded in Iranian political and economic life.
Iran's supreme leader Ayatollah Ali Khamenei praised the Guards on their National Day, saying they were at the "forefront' of defending the country and its interests, according to his official website.
He lashed out at US officials, saying: "Their vice and deceit will return boomerang on them, leading the enemies of the Islamic Republic such as (US President Donald) Trump and those around him at the US ruling apparatus to go down the drain."
To support his accusations, Rouhani cited the downing of Iran Air Flight 655 in July 1988 by missiles fired from the US naval ship the USS Vincennes.
"You have done everything imaginable. Which force was it that shot down our civil airliner in the waters of the Persian Gulf?" he said, adding that it was aimed at intimidating Iran.
"You wanted to tell the Iranian nation that we do not have any red lines, you wanted to say that we also kill children, you wanted to say that we also kill women," Rouhani said, concluding that the US was transmitting "a message of terrorism in the whole world."
The US move comes on top of Trump's decision last year to pull the United States out of an international deal with Iran that was meant to lift crippling economic sanctions in return for curbs on its nuclear programme.
Washington had been encouraged to blacklist the Guards by Trump's allies Saudi Arabia and Israel, which both cheered the declaration.
"The US decision (follows) the kingdom's repeated demands to the international community to address the issue of Iranian-backed terrorism," the official Saudi Press Agency quoted a foreign ministry source as saying on Tuesday.
The source welcomed the US move as a "practical and serious step" in curbing what the kingdom describes as Iranian meddling in the region.
The US decision came hours before an Israeli election in which Prime Minister Benjamin Netanyahu faces a close race for re-election.
In a statement, Netanyahu thanked his "dear friend" Trump who he said had responded to a "request of mine".
In a statement carried by the Iranian official news agency IRNA, the Supreme National Security Council declared the United States a "state sponsor of terrorism" and its forces in the region "terror groups".
Quickly adapting to the decision, the semi-official Fars News Agency, close to ultra-conservatives, described the US casualties in the latest suicide bombing on a military convoy in Afghanistan as "terrorists."
In a report on the attack, Fars said Tuesday: "American army terrorists killed in Afghanistan."
NATO announced on Monday that a suicide car bomb on a convoy in Iran's eastern neighbour had killed three US troops and a military contractor and wounded three more.