The tender follows a long-running review of air ambulance services across the country by the National Ambulance Sector Office (Naso), and it is seeking contracts for larger areas, including one for all of the South Island.
Also, for the first time, it requires operators to use twin-engined helicopters.
Mr Tapper said the Government needed to overrule its bureaucrats and rethink the decision.
"If they go ahead with this, and we get a death, I'm going to be the first person to jump up in the coroner's court and say, 'We told you so, you didn't listen, it's a load of . . . '.''
The trust contracts Te Anau-based Southern Lakes Helicopters and Heliworks Queenstown to have a helicopter on standby at all times. It provides accident and emergency and search and rescue cover for a large chunk of the southern South Island, including much of Otago, Southland, Fiordland and Mt Aspiring National Parks, Stewart Island and the Southern Ocean.
Mr Tapper said Southern Lakes Helicopters had the expertise and machines to take advantage of "little windows of opportunity'' in the weather to fly rescue missions that were impossible from Queenstown.
Its chief pilot, Sir Richard "Hannibal'' Hayes, had picked up two women on Friday from the Milford Track who were suffering from hypothermia.
The weather at the time had been "shocking'', with high winds and snow.
"One of the ladies was quite critical, and if she'd been left another hour or two she probably would've died.
"That's a classic example of having the right piece of gear in the right place at the right time, and having an experienced pilot who knows what he's doing.''
The tender's requirement for twin-engined helicopters was an "absolute nonsense'', he said.
They were much more expensive to buy and operate, whereas the "nimbleness and speed'' of the single-engined Squirrel helicopters flown from Te Anau gave them the ability to carry out rescues unsuitable for bigger machines.
Mr Tapper said three companies were considering bidding for the South Island contract: Heliworks in Queenstown, Dunedin-based Otago Helicopters and Garden City Helicopters in Christchurch.
Clutha-Southland MP Hamish Walker said it was "unacceptable'' to remove such an essential service from Te Anau, and he and other National MPs in the North Island who were similarly affected had requested a meeting with the Ministers of ACC and Health.
It was "unclear'' why Te Anau had been excluded, Mr Walker said.
The new operating model is expected to take effect on November 1.
