US Defense Secretary Jim Mattis on Monday dismissed Iran's threats of revenge against those behind Saturday's deadly attack on a military parade in southwestern Iran and said it was "ludicrous" for Tehran to allege US involvement.

Asked whether Iran's threat gave him any concern, Mattis told reporters at the Pentagon: "No, it does not. We've been very clear that they shouldn't take us on like that. And I am hopeful that cooler, wiser heads will prevail."

Iran's Revolutionary Guards Brigadier General Hossein Salami was quoted as saying the attack, which killed 29 people, had exposed the dark side of an alliance that the United States, Saudi Arabia and Israel had created to counter Iranian influence in the region.