Speaking before leaving Tehran to attend the UN General Assembly in New York, Rouhani accused US-backed Gulf Arab states of providing financial and military support for anti-government ethnic Arab groups.
"The small puppet countries in the region are backed by America, and the United States is provoking them and giving them the necessary capabilities," said Rouhani.
The attack was one of the worst ever against the Guards - the most powerful military force in the country - and is bound to ratchet up tensions with Iran's regional rival Saudi Arabia.
"Iran's answer (to this attack) is forthcoming within the framework of law and our national interests," said Rouhani, adding that the United States will regret its "aggressiveness".
An Iranian ethnic Arab opposition movement called the Ahvaz National Resistance, which seeks a separate state in oil-rich Khuzestan province, claimed responsibility for the attack.
"The Persian Gulf states are providing monetary, military and political support for these groups," said Rouhani.
Islamic State militants also claimed responsibility. Neither claim provided evidence. All four attackers were killed.
The assault, which wounded at least 70 people, targeted a viewing stand where Iranian officials had gathered in the city of Ahvaz to watch an annual event marking the start of the Islamic Republic's 1980-88 war with Iraq, state television said.
"Hopefully we will overcome these sanctions with the least possible costs and make America regret its aggressiveness towards other countries, and particularly Iran," said Rouhani.
The Islamic Revolutionary Guards Corp (IRGC) has been the sword and shield of Shi'ite clerical rule in Iran since its 1979 Islamic Revolution.
Hardliners such as the Republican Guards have gained standing at the expense of pragmatists in Iran's multi-tiered leadership since President Donald Trump decided in May to pull the United States out of the 2015 international nuclear deal with Tehran and re-impose sanctions on the Islamic Republic.