"Without doubt, those who have ordered and carried out this crime will have to await a harsh response that they will regret," that statement read.
The statement came after the Trump administration confirmed that it had assassinated Major General Soleimani, the commander of the Quds Force of the IRGC.
The attack also led to the death of Abu Mahdi al-Muhandis, the second-in-command of Iraq's Popular Mobilization Units (PMU).
The General Staff of Armed Forces' statement on Friday described the assassination as a "terrorist attack " carried out by the "criminal American regime".
"The brave commander, Major General Qassem Soleimani, played a key and unique role in fighting terrorist Takfiri groups which were set up by the criminal American government," it read.
The General Staff of Armed Forces offered its condolences to the "courageous people of Iran, Iraq and all the heroic fighters of the resistance axis".
The "resistance axis" is used to refer to an emerging front in the Middle East which includes Iran, Syria and other regional countries and forces such as Hezbollah, which are opposed to US and Israeli hegemony over the region.
Soleimani was known as a top figurehead assisting regional forces fighting foreign-backed terrorist groups in the region, notably in Iraq and Syria.
'US main loser of dangerous regional game'
Iran's First Vice President Es'haq Jahangiri said that the US' war mongering criminals will end up being "the main losers in this dangerous game in the region," following the assassination of Soleimani.
Jahangiri added that those following the path of Soleimani will "push away the fire of war, terrorism and division from the region".
"The name of Soleimani struck fear in the hearts of the enemies of the independence and freedom of Muslim nations," Jahangiri said, adding that Soleimani was an inspiration and cause for hope among the "truth-seekers" and "downtrodden" of the world.
Speaking earlier on Friday, Hessamoddin Ashena, adviser to Iranian President Hassan Rouhani, also said that Washington had "passed red lines" with the assassination and that it will "have to face consequences" of the attack.
"Trump, with his gambling, has pushed the US into the most dangerous regional circumstances. One who passes the red lines will have to be ready to face its consequences," Ashena said.