Meanwhile, The head of Iran's National Security Council said the country needed constructive dialogue to avoid tensions with neighbouring countries after an attack on a military parade on Saturday killed 25 people.
"We stand with the Iranian people against the scourge of radical Islamic terrorism and express our sympathy to them at this bad time", Nauert said.
"We will most certainly rigorously punish the perpetrators of this attack", he added.
Four assailants fired on a viewing stand in the southwestern city of Ahvaz where Iranian officials had gathered to watch an annual event marking the start of the Islamic Republic's 1980-88 war with Iraq.
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. In a statement on Sunday, the paramilitary organization said it knows where the attack came from, and threatened the masterminds "will face a deadly and unforgettable vengeance in the near future".
The father of 4-year-old victim Mohammad Taha lay atop his son's flag-draped coffin sobbing, a public display of grief near the Sarallah Mosque in Ahvaz, the capital of Iran's oil-rich province of Khuzestan.
Khamenei's remarks came as several of Iran's generals took tough tones to accuse the US of being involved in the attack.
U.S. State Department spokeswoman Heather Nauert said late on September 22 that the United States "condemns all acts of terrorism and the loss of any innocent lives".
"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", she told CNN.
The Islamic Revolutionary Guards Corps (IRGC) was set up after the 1979 Islamic Revolution to protect the Shi'ite clerical ruling system and revolutionary values.
It is, however, highly unlikely the Guards will strike any of its foes directly and risk setting off a regional conflict.
He wrote on Twitter: "Terrorists recruited, trained, armed & paid by a foreign regime have attacked Ahvaz".
They are also likely to enforce a tight security policy in Khuzestan province, arresting any perceived domestic opponents including civil rights activists.
Both Trump and Rouhani are attending this week's U.N. General Assembly in NY.
But the organisation said later on its website that the organization and its military wing do not assume responsibility for the attack on the military parade.
The U.S. wants Iran to "stop being the world's largest state sponsor of terror", Pompeo said.
Ayatollah Khamenei made the remarks in a meeting in Tehran on Monday with a group of athletes and medal winners of the 2018 Asian Games in Jakarta, Indonesia.
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