Gatwick claims Sir Howard Davies's decision not to back a second runway at the airport in West Sussex was flawed.
Sir Howard has written to the government insisting issues raised by Gatwick were carefully considered before the report was written.
The government is due to decide which airport should expand by Christmas.
The Airports Commission spent three years hearing submissions, including those from Gatwick and Heathrow, about how best to expand airport capacity in the South East.
Its report, on 1 July, said there should be a third runway at Heathrow.
Gatwick had argued strongly that it should be allowed to expand instead.
It has said the economic argument for expanding Heathrow is flawed and Sir Howard was using passenger numbers that were "10 years out".
Sir Howard forecasts Gatwick at 40 million passengers by 2024 but the airport says it will hit that number this year.
In a letter to Transport Secretary Patrick McLoughlin, Sir Howard says the Airports Commission believes strongly its work is robust.
"The majority of the points made by Gatwick Airport Ltd were also made to the commission in the course of its work and we considered them carefully before we reached our conclusions," he said.
Crispin Blunt MP for Reigate, who chairs a group of local MPs who oppose expansion at Gatwick hit out at the airport for continuing to campaign for expansion.
"Sir Howard Davies has demolished Gatwick's arguments, which amount to a feeble public relations effort to undermine the credibility of the Airports Commission's work and recommendations," he said.
Gatwick said it stood by its view that Sir Howard's report was flawed.
"If backed by government it will inevitably lead to 'Heathrow Groundhog Day' with nothing happening once again," said chief executive Stewart Wingate.
The chairman of the Airports Commission has rejected Gatwick's criticism of its report recommending expansion at Heathrow.