The celebrity gardener said he is “extremely disappointed” at their decision and has again requested the meeting take place.
And he said decisions on the redesigning and rebuilding of the garden in the city’s Fitzgerald Park which have been announced to the press “seem grossly flawed”.
Mr Gavin wrote to the city’s 31 councillors last week requesting permission for him and his design team from Diarmuid Gavin Designs Ltd to meet them, and to explain their side of the controversial saga.
It followed months of controversy over the taxpayer funded Avatar-inspired garden, which won gold at the Chelsea Flower Show last May but which was placed in storage in the city’s docklands area.
But councillors voted on Monday night against allowing the meeting take place.
They said it would be inappropriate to approve such a request from a contractor after the contractor’s project had been delivered.
But within hours of the vote, Mr Gavin’s company had sent a second letter to councillors.
His design studio manager, Helen Jones, said the firm started making requests to address the council as long ago as March 15, 16 and 20, in emails it sent to a senior city official closely involved in the project.
“We continued to make these requests to the city manager and Cork city’s solicitor,” Ms Jones said.
“This was well in advance of us building the garden at the Chelsea show.
“No contract has been completed as Cork City Council refused to issue one in the first place.
“Despite this, substantial funds have been allocated to creating the Irish Sky Garden at the Chelsea Flower Show.”
The letter continues: “It is our belief that as public money is involved, all parties should be held publicly accountable rather than dealing with these issues through the media.
“I am asking you, in the light of our first request being last March and not when ‘the project had been delivered’, to allow us to make a presentation to the council and answer questions.”
The Sky Garden is being 83% funded by Fáilte Ireland in the hope that it will become an iconic tourist attraction, once it is installed in Fitzgerald’s Park next year as part of a €1.8m refurbishment of the park.