The country star is scheduled to play five sell-out gigs at the venue from 25 to 29 July, but the council has ruled that two cannot go ahead.
More than 400,000 tickets have been sold.
Dublin City Council has said its decision to reduce the number of concerts cannot be amended or appealed.
Garth Brooks responded saying he'll do all five or none at all.
Sinn Féin wants Dublin City Manager Owen Keegan to take action.
Mary Lou McDonald, the party's TD for the area covering Croke Park, said the situation has been badly managed on many fronts.
"We believe, at this stage, that yes the five concerts should go ahead."
Ms McDonald said that Sinn Féin's Dublin councillors will ask for the council decision to be reversed.
Independent Dublin City Councillor Cieran Perry, said that the promoters didn't pay close enough attention to the early warning signs.
He said: "I met with Peter Aiken, with Aiken Promotions, I met with Croke Park and they were aware at the beginning of the year that this would lead to problems, the insistence on having this amount of concerts.
"So they were under no illusions."
He added: "Because they felt that the planning process was simply a rubber stamping exercise they felt that they could simply just plough along and ignore the concerns of residents."
On Saturday, Aiken Promotions told RTÉ that they will make a decision on Monday or Tuesday about what will happen with the shows.
Concert promoter Peter Aiken remains hopeful that all five would go ahead.
He said his company and authorities in Croke Park are "working behind the scenes" to try to stage all of the gigs.
Mr Aiken said: "The concerts aren't cancelled, but there's still a bit of hope. We are still working behind the scenes, both ourselves and Croke Park and I think that a final decision will have to be made Monday or Tuesday."
On Friday, the council said: "Dublin City Council has been consistent (since it was confirmed that tickets were sold for five concerts) in informing the promoter and his agents that its main concern was the impact that five consecutive concerts would have on the local area," the statement said.
"As the licencing authority, Dublin City Council must adhere to the procedures laid down in the attendant planning act and regulations.
"The decision to grant or refuse an event licence is made by senior management in DCC's Planning Department, to whom those powers have been delegated by the chief executive."