He could have been referring to Saudi Arabia, the United Arab Emirates or Bahrain - close USA military allies that view Iran as a regional menace over its support for militant groups across the Middle East.
According to state-run media, the attack killed 24 people, including 12 members of Iran's Revolutionary Guard Corps (IRGC), and wounded 53 others.
Ali Akbar Velayati, the Leader's adviser on global affairs, added that resistance of the Iranian nation and the Islamic establishment in the face of terrorist groups and extremist and Takfiri movements has led to the failure of all plots backed by the USA, the Israeli regime and some of their reactionary allies in the region.
No evidence was provided for either of the two claims. At least 18 people were killed and more than 50 wounded in the attacks.
A Revolutionary Guards spokesman claimed the attackers were "trained and organised by two Gulf countries" and had ties to the United States and Israel.
"Terrorists recruited, trained, armed & paid by a foreign regime have attacked Ahvaz", Zarif said in a tweet, adding: "Iran holds regional terror sponsors and their USA masters accountable for such attacks".
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The attack took place on a day when military parades were being staged across the country to mark the anniversary of Iran's eight-year war with Iraq in the 1980s.
Iran's Foreign Minister Mohammad Javad Zarif immediately blamed the attack on regional countries and their "US masters," further raising regional tensions as Tehran's nuclear deal with world powers is in jeopardy after US President Donald Trump withdrew America from the accord. In November 2012, Iran's Ministry of Intelligence said it had arrested several members of a "terrorist group" operating in Khuzestan that had planned at least three bombings in Ahvaz targeting government offices and banks.
Ahvaz is the capital of the oil-rich province in Iran's southwest.
Abdulkhaleq Abdulla, an advisor to Emirati Crown Prince Mohammed bin Zayed, justified the attack writing on Twitter: "attacking a military target is not a terrorist act" and "moving the battle deeper inside Iran is a declared option".
Earlier on Saturday, local media reported that in a 10-minute attack, gunmen wearing military uniforms fired at Iranian forces in a military parade.
Armed forces spokesman Brigadier General Abolfazl Shekarchi said the dead included a young girl and a former serviceman in a wheelchair.
An Ahwazi political group refuted claims that ISIS carried out the deadly attack on the military parade.
Hardliners like the IRGC 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 worldwide nuclear deal with Tehran and reimpose sanctions in moves to isolate the Islamic Republic.