Among those buried was Mohammad Taha Eghdami, a four-year-old boy, who was the youngest victim of the attack.
Of the 25 killed, a dozen were members of the Islamic Revolutionary Guard, the country's elite security and military organization.
Describing the attack on defenseless people as an act of cowardice, the Leader noted, "According to [available] reports, this cowardly act has been perpetrated by the same people who are saved by Americans whenever they face a hard situation in Iraq and Syria" and whose operations are being financed by Saudi Arabia and the United Arab Emirates.
Both Isis (Islamic State) and the Ahvaz National Resistance, an Iranian ethnic Arab opposition movement which seeks a separate state in oil-rich Khuzestan province, claimed responsibility for the attack.
While mourners gathered at a funeral procession in Ahvaz on Monday, Intelligence Minister Mahmoud Alav promised revenge against those responsible.
"This cowardly act was the work of those very individuals who are rescued by the Americans whenever they are in trouble and who are funded by the Saudis and the (United) Arab Emirates", Khamenei's official Twitter account quoted him as saying.
Haley said Washington was trying to counter Iranian malign activities in the region as Tehran continued to test ballistic missiles, support terrorism and sell arms.
Hossein Salami, deputy head of Iran's Revolutionary Guards, blasted the United States, promising "devastating" revenge.
Iranian armed forces members and civilians take shelter.
"Considering (the Guards') full knowledge about the centres of deployment of the criminal terrorists' leaders., they will face a deadly and unforgettable vengeance in the near future", the Guards said in a statement carried by state media on Sunday.
Iranian military mourn over the bodies during a public funeral ceremony for those killed during an attack on a weekend parade.
Khamenei's remarks came as several of Iran's generals took tough tones to accuse the USA of being involved in the attack.
The United States was not the only country to delay its messages of condolences to Iran - notably, unlike many other nations, it does not have an ambassador in Tehran.
There has been a blizzard of furious statements from top Iranian officials, including President Hassan Rouhani, accusing Iran's adversaries the U.S. and Gulf states of provoking the bloodshed and threatening a tough response.
It answers to Ayatollah Khamenei and has an estimated 125,000-strong military with army, navy and air units. But it is unlikely the IRGC will strike any of these foes directly.
Iran's Foreign Ministry earlier summoned the UAE charge d'affaires over comments made about the bloody fusillade at the military parade, state-run PressTV said.
Iran is at odds with Western-allied Gulf country Saudi Arabia for predominance in the Middle East.