SkyCity is believed to be seeking about 400 additional poker machines, greater use of "ticket-in ticket-out" technology which increases gambling revenues, and an early renewal of its exclusive right to run the only casino in Auckland.
The Greens and Labour yesterday called for the negotiations to be suspended until the inquiry was complete.
But Economic Development Minister Steven Joyce said the Government was "very relaxed" about the inquiry. "We don't see any reason to delay negotiations."
Mr Joyce said he would be "not at all concerned" about signing a deal with SkyCity even with the inquiry in progress. However, Government sources said any deal struck was unlikely to be publicly announced until the inquiry was completed.
In any case there was little expectation the deal would be completed before the inquiry was finished, the source said.
Interviewed on Radio NZ yesterday, Mr Joyce refused to say what the Government would do if the inquiry identified concerns around the deal.
Labour leader David Shearer said Mr Joyce was being "extraordinarily arrogant in continuing to run this process".
"To me it beggars belief that he can continue to do this while an inquiry is going on. Not only should negotiations go on hold until the inquiry is complete, but the tender process should restart from scratch."
Meanwhile, news of the probe has heightened fears SkyCity might walk away from the deal.
Negotiations with SkyCity have been continuing for about a year and a source close to the talks told the Herald that executives at SkyCity were becoming exasperated with the details over which Ministry of Economic Development officials had laboured.
The source said officials told SkyCity they wanted a clear separation between the convention centre business and the casino and hotel business, which were directly across the road from the proposed building site.
Frustrations had increased when, at a meeting about two months ago, officials from the MED produced architectural drawings which it had commissioned. The drawings were substantially different from SkyCity's, which had been overseen by the same experts who had designed the casino, hotel and Sky Tower complex.
SkyCity chief executive Nigel Morrison has told shareholders the company had made allowances to fund the deal if its negotiations with the Government went as hoped.
But Alan Trotter, chief executive of industry marketing organisation Conventions and Incentives NZ, said he was concerned the deal and the money which went with the SkyCity deal might slip away from New Zealand.
"My fear is SkyCity will say the $350 million is clearly not required by New Zealand - we will take it offshore.
It is not a given the money will be spent at the other [SkyCity] sites in New Zealand. You can't just keep them hanging on.
"The objections around the process are mischievous and they are a distraction. We run the risk of looking a gift horse in the mouth."
SkyCity's share price fell 3.4 per cent after the announcement of the inquiry.