But the Government is also indicating that pumping in public money beyond the original $402 million costing is its "least preferred option".
Mr Key had said that a centre built for the initial figure could be an eyesore. However, yesterday he said: "The Government's preferred position is that SkyCity completes the convention centre for $402 million."
The change did not prevent continued attacks from the Opposition, with ally the Act Party also labelling the deal a poor one.
On the same day SkyCity announced multimillion-dollar profits, the Government backed away from recent indications it would put in taxpayer money.
The ongoing focus on the deal came as SkyCity chief executive Nigel Morrison said the casino operator was open to contributing more money to fund the centre.
At the announcement of SkyCity's half-term results, Mr Morrison hinted that it might be negotiating with the Government to pay more.
Asked how much extra the casino might contribute to a more expensive centre, Mr Morrison said: "I'm sure it will come out in due course."
He rejected claims SkyCity had been manipulative.
"We certainly have not played the Government. The Government has been a very tough negotiator."
Mr Morrison said the $470 million-$530 million estimate was a combination of rising building costs and enhancements to the centre.
He emphasised that SkyCity had beaten all other parties to the deal.
"There is nobody else coming forward and offering to pay for this convention centre ... the land is worth over $100 million."
Finance Minister Bill English yesterday said if any money was put up to meet the over-run it would be factored into the new Budget, which will be delivered on May 21.