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A majority of councillors voted last week to reduce the capacity of the $473 million covered stadium to 25,000 seats from 30,000 due to a budget blow-out.
An online petition calling on the city council to reverse the decision has reached more than 20,000 signatures.
But deputy mayor Andrew Turner, who voted to reduce the capacity, said cutting the number of seats was the right decision.
"The reasons for the decision that we took last week remain," he said.
"That particularly relates to the quality of the experience at the arena in Christchurch, the right-sizing of the arena for the content that we want and expect to be able to attract to Christchurch with a 25,000-seat arena."
He said the estimated budget blowout of $88 million would have been a huge burden for the city.
Councillor James Gough, who wanted to keep the 30,000 seats, attacked the decision after the 22 July meeting.
"At the end of the day, a stadium or multi-use arena isn't just because we want to blow hundreds of millions of dollars to watch people kick balls around, it's because of the catalyst effect that has on a local economy."
New Zealand Rugby had earlier warned the council that reducing the indoor stadium size to 25,000 would make the arena too small for major international rugby games, unless a substantial incentive fee was on offer.
The stadium is scheduled to open in 2024.