Iranian Supreme Leader Ayatollah Ali Khamenei said the United States had made "a vicious move" in designating the Revolutionary Guards as a foreign terrorist organisation, and Tehran vowed to take action against US forces in the region.
This is the first time the USA has designated a foreign military unit as a terrorist outfit.
But Saudi Arabia - one of Iran's rivals - praised the United States' decision, calling it a "serious and practical step to combat terrorism". He said the organization was at the "forefront" of national defense and claimed the "vice and deceit" of American officials "will return boomerang on them".
"You use terrorist groups against the peoples of the region and yet claim to have been fighting terrorism?"
"Who are you to label revolutionary institutions as terrorists?" he asked.
The IRGC is estimated to have more than 150,000 active personnel, boasts its own ground forces, navy and air force, and oversees Iran's strategic weapons, including its ballistic missiles.
Iran's most elite military unit, the IRGC was set up shortly after the 1979 Iranian revolution to defend the country's Islamic system, and to provide a counterweight to the regular armed forces.
They added that "Iran is the world's leading state sponsor of terrorism, and the IRGC is the primary vehicle through which the regime funds terror organizations and proxies overseas".
Trump's move comes after relations between Tehran and Washington took a turn for the worse last May, when Trump pulled out of a 2015 nuclear deal between Iran and six world powers and reimposed sanctions.
The source welcomed the USA move as a "practical and serious step" in curbing what the kingdom describes as Iranian meddling in the region.
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".
Iran has so far continued to comply with the nuclear deal, but its clerical rulers have threatened to withdraw from it and to resume the suspended Iranian uranium enrichment programme if other signatories to the pact fail to protect Iran's interests.
Iran's supreme leader, Ayatollah Ali Khamenei, who has the final say on all state matters, met members of the Revolutionary Guards on Tuesday, telling them: "Americans imagine they are designing and making trouble against the guard - in fact against the revolution and Iran - but their evil designs will not harm [the force]".
Co-signatories Britain, France and Germany are trying to salvage the nuclear deal and set up in January a mechanism to allow trade with Tehran and circumvent US sanctions.