Grey Power wants Kiwibank to fill the void left by the closure of physical branches belonging to the commercial banks.
Around 100 people last weekend protested ANZ's departure from Martinborough, leaving the tiny Wairarapa town without a bank from October 19.
ANZ said 80 percent of its customers in the town hadn't used the branch in the past year, and in-person transactions are on the decline. The bank says it spent $200 million in the past four years upgrading its mobile and internet options.
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But Grey Power is worried about the elderly who can't or won't use mobile and internet offerings.
"Many senior people don't use internet banking or emails for communication and many don't even have computers," said president Mac Welch.
"The bank and the local post office, or post shop, are the centre of many small communities. It is where people conduct most of their official business and local bankers and postmasters know what service means."
He said once the banks leave, service stations and schools may soon follow.
South Wairarapa Mayor Viv Napier agrees, saying banks have got their blinkers on.
"Why should you disadvantage a percentage of your clients because they can't access the technology that you want to use? They should be looking across their whole client base," she told Newshub.
But Kiwibank says the average customer visits a branch only one or two times a year, but uses online or mobile banking almost every day.
Ms Napier says going to a bank should be easy for everyone.
"From Martinborough to Masterton, where the nearest ANZ Bank is, is a one-and-a-half-hour trip. Well that's ridiculous, to have to go and do some banking in a branch."
Kiwibank says it has opened nine branches in the past year and customers prefer 24/7 service.
"We have a responsibility to New Zealand to be a sustainable, relevant and economically viable business and we need to be proactive in adapting to the rapidly changing marketplace in which we operate," the bank said in a statement.
Kiwibank says it hasn't had any correspondence from the Government on the matter.
An earlier version of this article incorrectly stated that Westpac is currently in the process of closing a number of branches. This actually happened in 2016.