Foreign Minister Mohammad Javad Zarif immediately blamed the attack on regional countries and their "US masters", further raising regional tensions as Teheran's nuclear deal with world powers is in jeopardy after President Donald Trump withdrew America from the accord.
On Twitter, Mr Zarif warned that: "Iran will respond swiftly and decisively in defence of Iranian lives".
The death toll of 24 was expected to rise after gunmen attacked the parade in Khuzestan province on Saturday, according to deputy governor Ali Hosein Hoseinzadeh.
Ahvaz is the capital of the Khuzestan province, which borders Iraq and is home to a large Sunni population and some of the country's largest oil fields.
No group has yet claimed responsibility for the attack, but a spokesman for the Revolutionary Guards pointed the finger at ethnic Arab separatists.
An Arab opposition movement called the Ahvaz National Resistance and Islamic State (IS) militants have both claimed responsibility for the attack.
Brigadier General Abolfazl Shekarchi was quoted by IRNA as saying the terrorists were "not from Da'esh (ISIS) or other groups fighting (Iran's) Islamic system ... but are linked to America and the [Israeli global intelligence agency] Mossad". Two of the Al-Ahwazi terrorists killed, one wounded & arrested, and another arrested alive. It was the deadliest such attack in Iran in almost a decade.
An Iranian soldier carrying a child to safety
A woman and a child were among at least 20 people wounded in the attack by a "group of assailants" on the parade in the city of Ahvaz, the official IRNA news agency reported.
He said the British diplomat had condemned the attack and said he would relay Tehran's message of protest to the authorities in London.
Iranian government and military officials have pointed the finger at Gulf states, the USA and Israel, with all of whom Iran has longstanding tensions.
Turkish President Recep Tayyip Erdoğan conveyed his condolences to the people and government of Iran following the armed attack.
However, Emirati academic Abdulkhaleq Abdulla, has tweeted on the Ahwaz attack by saying: "A military attack against a military target is not a terror act".
The group is supported by "foreign antagonists", including Saudi Arabia, the agency said.
His remarks could refer to Saudi Arabia, the United Arab Emirates or Bahrain - all close USA military allies that consider Iran a menace because of its support for militant groups in the Middle East. Every ounce of money that goes into Iran goes into his military.
Some 60 people were wounded in the attack, a lot of them civilians.