U.S. Department of Homeland Security Secretary Markwayne Mullin said he is "so happy" that Iran are out of the World Cup in remarks that the country's football federation described as "hostile."
Iran's participation in the tournament was uncertain in the months leading up to it after the U.S. and Israel launched airstrikes on the country in February.
However, Iran did take part and came close to qualifying for the last 32 after drawing all three group games but were denied victory against Egypt in their final game by a marginal offside call.
The federation made multiple complaints over Iran's treatment by U.S. authorities during their time at the competition, with coach Amir Ghalenoei saying his team was the "most oppressed" at the World Cup.
On Tuesday, Iran said their treatment at the World Cup "undermined the sense of fairness."
Mullin admitted during a World Cup security briefing: "I'm just glad they're done, and they're not coming back.
"I was so happy when we were able to pull their visas and said they could leave the U.S. soil, and I might've sung a song or two or maybe even danced a happy dance."
Iran's football federation responded with a statement in which it said it was unsurprised by the U.S. official's comments and said they underscored the fact they had never been welcome at the tournament in the first place.
"Iranians are used to the mistreatment and lies of U.S. officials, so no one in Iran is surprised by these hostile remarks," Iran said in a statement that also referred to a missile strike in the country that remains under investigation by U.S. authorities.
The federation added: "These remarks once again demonstrate that U.S. officials have no commitment to international law or the principles expected of a host nation capable of organizing a global sporting event.
"The fact that he openly celebrates Iran's elimination says far more about him than it does about our team. It reflects a level of pettiness that cannot even tolerate the presence of a football team competing on the world's biggest stage.
"After our match against New Zealand, our head coach said that the United States did not want Iran to remain in this tournament because of the inhumane and unprofessional treatment our team experienced. These latest comments only reinforce that belief."
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Iran moved their training base to the Mexican border city of Tijuana in May, having originally been due to be based in Tucson, Arizona. All three of their matches were played in the U.S. -- with the first two in Los Angeles and the last one in Seattle.
One of Iran's complaints during the World Cup was the stipulation from the authorities that they leave immediately after each match.
Asked about that, Mullin said: "That was just an agreement we had -- to just go ahead and let them go.
"The game was over, let them get back to the hotel, their base camp where they're at. They're more comfortable there. That was just an agreement we worked out with FIFA before the games started."
Mullin said "almost half" of Iran's non-playing delegation had direct ties to the Islamic Revolutionary Guard Corps (IRGC).
FIFA have been contacted for comment.
The Iran team left a handwritten note addressed to the people of Mexico that read: "You showed us that hosting a FIFA World Cup is about far more than stadiums and tickets.
"True hosting is about respect, humanity, and dignity. We will never forget the kindness of the people of Tijuana. From this day forward, Mexico will always be more than a host nation to us; it will be our second home and our second team.
"We leave this World Cup with pride, but also with one fundamental question: Did every team truly compete under equal conditions and equal professional standards?
"What we experienced was a series of decisions, logistical arrangements, and circumstances that undermined the sense of fairness -- an impression only reinforced by the events of the final matchday of our group."