The British architect has accused Milan officials of ignoring his design and installing a poor quality stone floor throughout the £44 million complex, which is due to open later this month in the Italian city.
This, Chipperfield said, has resulted in a finish that is "unacceptable" and has forced him to publicly disown the project.
"It is a pathetic dispute at the end of 15 years work. However I can do no more," he said in a statement sent to Dezeen. He also urged taxpayers to demand the building be finished to the standard that was promised.
The Città delle Culture (City of Culture) complex occupies a converted steel factory in Milan's Tortona district. It is expected to open on 26 April, coinciding with the 2015 World Expo that opens the following week.
Reports of the "war of the floor" surfaced in the Italian press last month, when culture minister Filippo Del Corno told L'Espresso magazine that Chipperfield had been difficult to work with. The architect responded by branding the project a "museum of horrors" in a press conference, according to a report by UK newspaper the Independent.
Chipperfield – whose completed museum projects include the Neues Museum in Berlin and the Hepworth Wakefield gallery in northern England – has now accused Del Corno of lying and contriving to make him look like "an unreasonable and impossible collaborator".
"The explicit lie saying that I had demanded the floor to be taken up forces me to expose the rather miserable story behind such a simple problem, and explain our exhaustive attempts to solve this problem," he said.
"I must point out that this dispute has been running for nearly 18 months, at no point did we resort to any strategy other than trying to resolve the physical mistakes made to the building," he added. "It is sad that the public administration has spent so much time avoiding responsibility and so little time solving the problem."
He also defended himself over claims that he was acting selfishly. "Architecture only speaks through results, and we were willing to participate in this process," he said.
"Please be assured that my 'Italian career' wasn't motivated by a desire to become rich but to work in a society that has a deep history and profound understanding of the importance of architecture, the city."
The stone covers 5,000 squares of flooring inside the building, but is reportedly scratched, stained and misaligned. According to Chipperfield, it was chosen against his specification, and against the bid from the building contractor.
"The stone contract was not properly supervised and the resulting quality was in my opinion unacceptable," he said.
He claimed a specialist team recommended that the problem could be fixed for €300,000 (£219,000) – and even offered to cover half of the cost, out of the fees still owed to him by the client. But he claimed the city council wanted the work done for free.
"That was the situation in last September after months of work and collaboration," he said. "As of today the specialists have not had any further correspondence and nothing has been done to the floor."
Chipperfield also claimed his firm has been working over the last three years for no fee, and said that the floor was the "most extreme case" in a string of problems that included substandard concrete finishes.
"Despite the fact that the process was at times exceptionally frustrating, despite the fact that the project started and stopped many times and despite the fact that the public administration began construction without engaging us in 2009, despite the fact that we have attended the project for the last three years with no fee at all, and the previous two years we were paid just over €100.000, despite all these frustrations, we were, 18 months ago quite satisfied by what had been achieved," he said.
"After some remedial work and good collaboration we managed to get good concrete, the facade is good as the central space. All that was missing were the finishes, the surfaces, floors, panelling, graphics."
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"Unfortunately nine months later another level of frustration had been established," he added. "Once the floor was made visible it wasn't a difficult argument to make. In fact over this last 12 months that we have been trying to resolve the situation, no one has attempted to deny that the floor is unacceptable."
The city council has defended the project, insisting that budget decisions were all based on "common sense". It claims that Chipperfield's firm approved the material before it was installed, and also alleged the architect has accepted over £2 million in fees.
"It cost €60 million, of which €3.6 million went to Chipperfield for his design and project management," the council said in a statement. "These are sums of money appropriate for a public institution and right for the importance of the project, but it was necessary to make choices based on common sense and in the interests of the taxpayers."
It added: "The samples and the visits to the quarry supplying the material were overseen by staff of the office of David Chipperfield Architects, who validated the choice of the material used."
Designed as an mix of two-, three- and four-storey volumes framed by courtyards and passages, the Città delle Culture will house the Centre for Advanced Studies of Visual Art (CASVA), the Centre of Non-European Cultures and the New Archaeological Museum.
Photography is by Oskar Da Riz.