Detectives said a man arrested afterwards with a handgun had been paid by one of the gunmen to take the weapon.
A second firearm, an improvised shotgun — believed to have caused the two injuries — was recovered earlier at the scene.
Gardaí said the mayhem — which also saw a man badly injured by a slash- hook — was part of a Traveller feud and linked to previous incidents in Waterford and Galway.
It emerged yesterday that Gardaí had asked Dublin City Council (DCC) to ban the monthly Smithfield Horse Fair and had done so previously in 2009.
The DCC said it doesn’t have the power to do so and that it had asked the outgoing government to change the law protecting the event, but without success.
The Garda Síochána is likely to raise the matter formally at a senior level and both the DCC and Dublin Lord Mayor are to lobby the new government to change the law and ban the fair.
Pavee Point Travellers’ Centre said it would be “a disaster if one, admittedly serious, incident” should end a longstanding tradition for the Smithfield area and called for the event to be regulated.
The March event is the largest of the monthly fairs and 4,500 adults and children were crammed into the Smithfield plaza, along with the horses, on Sunday.
Liam Kinsella of the Dublin Society for the Protection of Cruelty to Animals (DSPCPA) said he was just yards from the shootings, at 11.30am.
“It was absolutely terrifying, people trampling on each other, horses let loose, absolute pandemonium.”
He said mothers were trying to “pull children out of buggies” and he was “gob- smacked” no one was seriously injured.
Two members of a family from Co Offaly were hit in the body with shotgun pellets, while a third man received injuries to his left arm from a slash-hook.
Gardaí said it took “some time” to identify all those involved and that they had not received consistent cooperation from everyone.
Inquiries, including evidence from video cameras, led them to nearby Oliver Bond flats, where they recovered a handgun and arrested a man, who had been paid to take the gun.
Detectives believe they have identified the two gunmen and are confident they will track them down.
Dublin Lord Mayo Gerry Breen said he would be writing to the new minister for justice this week requesting legislation be brought in to “abolish” the horse fair.