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Gisborne Mayor Rehette Stoltz said banks must consider more than just economics when it came to closing branches.
It was a view backed by 32 other mayors who signed a letter to Prime Minister Jacinda Ardern calling for the government to intervene.
They said access to an ATM did not address "the social harm and problems" caused by closing branches supporting provincial communities and economies.
South Wairarapa Mayor Alex Beijen, who wrote the letter and has rallied the support of others across the country, said his district had experienced a "full withdrawal" of banking branches.
"An area of nearly 3000 sq/km without a single bank," he said.
Beijen is expected to pass the letter to a minister at a meeting at the Beehive this week.
It comes as Kiwibank last week announced plans to close seven branches including Gisborne over the next year, in a response to more customers moving online to do their banking.
Bank of New Zealand in November last year announced its plans to close 38 branches.
Stoltz said Kiwibank's plans were of "great concern".
"I know that this proposal will cause upset especially among our older residents as they value the face-to-face service, and might also not be tech-savvy enough to navigate their way via internet banking and the Kiwibank app.
"We also need to remember that some members of our society are not able to use phone or internet technology and need banking assistance.
"Our community needs and deserves to be serviced by our only state-owned bank in a fit-for-purpose way - face-to-face, phone, internet and via an app.
"Kiwibank will need to consider more than just its economic reasons," she said.
"If the prime minister agrees to an inquiry and the inquiry highlights these negative impacts, the government should require that all major commercial banks operating in New Zealand - as part of their licence to operate - be required to provide a level of service that redresses these issues," Stoltz said.
Kiwibank announced the proposed branch closures at the same time as its half-year result which saw its net profit rise $4m to $55m for the six months to December 2020.
A Kiwibank spokesperson said that for every 1000 transactions or activities at Kiwibank, 977 are digital, 15 were via ATM, five were in-branch and three were through their contact centre.
There are 3.5 fulltime equivalent roles at the Gisborne branch and they were working through options with the team, including the possibility of redeployment.
Tairāwhiti Technology Trust treasurer Maurice Alford last week said it was a "kick in the guts for the already disenfranchised".
"From our experience working with older people transitioning to the digital world, they're like foreigners," Alford said.