One element of the Saarinen building will almost certainly not be salvaged: the trumpet-shaped flight departure lounge that used to sit at the end of one of the tubular corridors. Last year, at a cost of about $800,000, it was cut apart from the rest of the structure and moved about 1,500 feet to get it out of the way of construction crews while preservationists, airport officials and airline executives tried to figure out if it could be reused.

Though Mr. DeCota declined to say flatly on Thursday that nothing could be done with the trumpet structure, he hinted strongly that the money needed to renovate it — which he put at more than $10 million — would be better spent on the Saarinen head house.

The Municipal Art Society, a civic organization that belongs to the redevelopment advisory committee involved with the Saarinen building, believes that any decision to destroy the trumpet structure would be “premature, fiscally irresponsible and historically inappropriate,” said Frank E. Sanchis III, the society’s senior vice president.

Mr. Sanchis said that the fate of the trumpet was discussed without consulting the redevelopment committee and that the cost estimates were inflated. On Thursday, the art group appealed to the federal Advisory Council on Historic Preservation in Washington to intervene