Michael Gove's call for Sheffield Council to stop cutting down trees could cost the city over a million pounds, the authority has said.
The environment secretary wrote to the council last week urging it to stop the felling and replacement programme that makes up part of the 25-year Streets Ahead PFI contract with Amey.
Mr Gove raised concerns about the transparency of the decision making process, adding: "The destruction of thousands of mature trees from the steel city will surely damage our children’s rightful inheritance."
But the council says the consequence of making major changes to the contract would be 'detrimental' to city residents.
Director of culture and environment Paul Billington said: “Ending the programme would have huge environmental and financial consequences for the council and Sheffield’s taxpayers, a knock on effect on the city-wide programme, leaving roads and pavements unsafe and furthermore, would put the council in neglect of our legal duties.
“The programme has been challenged three times in court and has been found to be legal on all occasions.
"Ultimately, the contract is a vital investment for our city which will ensure improved roads and pavements with an increased street tree stock which can be enjoyed by future generations.”
The council says the financial penalty for renegotiating the contract as Mr Gove suggested would be at least £1 million.
Cabinet member for environment Bryan Lodge has invited the minister to visit Sheffield and see the issues for himself.
The authority has also warned of further costs to the taxpayer should Amey not meet its targets by the end of the five year 'core investment period' of Streets Ahead, which finishes on December 31st this year.
The council says tree felling in particular has been held up by campaigners taking legal action and protesting inside safety barriers, and the taxpayer will bear financial consequences if targets - including the felling of 6,000 of the city's 36,000 street trees - are not met.
The authority claims the 'majority' or Sheffield residents are in favour of the tree work, but campaigners disagree. They say the council is cutting down healthy trees in order to save money. Independent experts have also questioned Amey's assessment of trees due to be felled.
Three campaigners - Dave Dillner, Calvin Payne and Coun Alison Teal - are expected to find out tomorrow whether or not a council injunction to stop them going inside safety barriers has been successful.
Sheffield Tree Action Groups co-chairman Rebecca Hammond said there were engineering solutions within the Streets Ahead contract that meant trees could be retained while roads and pavements were resurfaced - but there were not being used.
"All the evidence suggests that the tree-felling programme is intended to save on maintenance costs for Amey, not provide benefits to the people of Sheffield," she added.
And fellow co-chairman professor Chris Rust said the Streets Ahead contract should be made fully available for public scrutiny, adding: "It is very worrying that our council have signed up for a 25 year contract with no chance for renegotiating the details without heavy costs.
"Nobody can predict that far ahead. But actually we get the impression that Amey is much more flexible over tree decisions than the council and it's perplexing why so many healthy trees are condemned for reasons that independent experts, as well as concerned citizens, cannot understand."