Four gunmen disguised as military personnel opened fire on the parade which was commemorating the anniversary of Iran’s eight-year war with Iraq in the 1980s.
Among the 29 slaughtered were members of Iran’s Revolutionary Guard, soldiers and civilians, including children.
Two groups have claimed responsibility for the attack — Islamic State and the separatist group Ahvaz National Resistance — but neither has provided evidence.
The brutal attack has ignited a fierce war of words, as tensions across the region mount.
How is the US involved?
Iranian President Hassan Rouhani said on Sunday the «bully» US, along with Gulf states it backed, had enabled the attack.
He said: “It is perfectly clear to us who were behind the attack and what their affiliation is.»
The Iranian President alleged a Gulf country had supported the «financial, weaponry and political needs» of the attackers.
He added: «The small puppet countries in the region are backed by America, and the US is provoking them and giving them the necessary capabilities.»
Mr Rouhani did not lay out exactly which “puppet” country he referred to, but it is widely thought to be directed at Iran’s regional foe Saudi Arabia, and the UAE and Bahrain.
Iran and Saudi Arabia have a long history of conflict, engaging in proxy wars in the Middle East for decades.
The UAE and Bahrain are closely allied with Saudi Arabia.
Iran has also alleged that the gunmen had links to Israel.
The White House responded to Mr Rouhani’s accusations, calling them “baseless.”
Nikki Haley, US ambassador to the UN, said: «He’s got the Iranian people… protesting, every ounce of money that goes into Iran goes into his military, he has oppressed his people for a long time and he needs to look at his own base to figure out where that’s coming from.
«He can blame us all he wants. The thing he’s got to do is look in the mirror.»
Tensions between Iran and the US are not new.
There has been a bristly relationship marked by distrust between the countries for decades.
Things began to flare up notably this year when President Donald Trump withdrew the US from the Iran Nuclear Deal.
Since then, the US has brought sanctions back into place, despite opposition from EU partners, China and Russia, and warned that anyone trading with Iran would also be punished.
The move was backed by Saudi Arabia, and Iran accused the US of escalating the conflict between the countries.
Mr Rouhani will face Mr Trump at the UN General Assembly this week.