Councillors and Mr Parker refused to discuss the meeting with The Star yesterday.
Mr Brownlee confirmed that the meeting had taken place, but would not give specifics as to what he told city councillors.
"You are asking me to release it all and I'm not going to do that," he said.
"Councillors do need to have time to think of the implications for ratepayers," he said.
In September the Government announced a $1.1b five-year repair plan for earthquake damaged roads and underground services.
But The Star understands the Government is now worried that figure could balloon several times over because of the extent of the unknown damage.
The Star has learned Mr Brownlee told the meeting that no one knew how the cost was going to be met - whether through rates, selling off assets or raising loans.
Mr Brownlee told The Star yesterday city councillors "needed time" to consider the impact on ratepayers.
But Mr Brownlee said that "80 per cent was misleading''.
"I'm sounding a bit flustered here but everything is based on a best available information and estimates. We think 12 per cent of the underground infrastructure has been completed and there is billions of dollars of work currently being planned. The estimates are more like 50 per cent is known and that is conservative, I feel it could be as high as 60 per cent."
Mr Brownlee said the cost of repairing the underground infrastructure would not be known until the work was finished.
"All I can say is that when it is finished we will know the cost," he said.
"Until we get the digger out we can't fully know the cost," he said.
Mr Parker could not comment on the meeting as he did not want to lose Mr Brownlee's confidence.
"I think he should respond and explain his rationale as it was his meeting. If you are invited to a confidential meeting you accept it and be party to the information or reject it," said Mr Parker
"The minister called the meeting because he had information he wanted to pass on that was material to the rebuild.'' City councillor Tim Carter said that discussing the meeting "was very delicate".
"It is something which is very delicate and one which I don't want to comment on.
"What I can say is that I am very concerned with council's finances and the lack of information the council has," he said.
"I'm concerned that council is not getting true and accurate information about insurance pay outs and the true cost which council is liable for," he said.
Labour's earthquake recovery spokeswoman, Christchurch East MP Lianne Dalziel, said she was concerned the meeting was held in secret.
"That is a very old-fashioned way with dealing with these matters. It is vital for the rebuild that there is transparency and accountability right the way through instead of the minister having private meetings with city councillors behind closed doors," she said.
"I honestly believe that part of this process has to be that central government stops being heavy handed and stops talking behind closed doors and comes into an environment where there is complete transparency.
"These figures for the rebuild are eyewatering but it is better that they are out in the light instead of in the dark," she said.
"The need for transparent processes is vital otherwise people will get concerned about council selling revenue generating assets," she said.
