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Te Anau was one of three bases cut from a list of bases in a tender for air rescue services put out by the ACC and Ministry of Health last month.
Taupo and Rotorua’s bases were effectively restored to the list after three North Island mayors met Mr Clark on Monday.
However, Mr Walker said his requests to Mr Clark and ACC minister Iain Lees-Galloway for meetings had been stonewalled.
The latter told him it was "not his role" to get involved, and Mr Clark told him "he doesn’t have time to fit me into his schedule".
"The people of Clutha-Southland will be very disappointed to hear the Minister of Health hasn’t even got the time to hear concerns of the community.
Te Anau’s base was in a more critical location than the two North Island ones, which were nestled between other bases.
"It’s not only covering Fiordland, but the Muttonbird Islands and Stewart Island. It’s a huge area."
The tender follows a review of air ambulance services across the country by the National Ambulance Sector Office on behalf of the Ministry of Health and the ACC.
Mr Clark’s office was approached for comment but did not respond by deadline.
It is seeking contracts for larger areas, including one for all of the South Island, and requires operators to use twin-engined helicopters.
Submissions on the proposal close on May 7 and changes are to take effect from November.
Federated Farmers president Katie Milne said in a media statement feelings were "running high" in Te Anau, Fiordland and Haast over the issue.
Operating the rescue service from Queenstown would add 20-25 minutes’ flight time to that from Te Anau.
"We know every minute counts in the so-called golden hour after a serious accident or emergency, and that’s assuming the weather is playing ball and a helicopter from Queenstown can get up and over the mountains.
"Local knowledge of terrain and conditions can be absolutely vital when the search is on for an injured farmer, road smash victim or hypothermic tramper."