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IAG proposes to close its 53 AMI branches across New Zealand, as well as its sole remaining State Insurance branch, in Christchurch.
The Dunedin, Mosgiel, Gore, Queenstown, Invercargill and Oamaru sites are lined up for closure under the proposal.
Consultation had begun with affected staff, and the company hoped to retain many of them.
IAG expected to move more than 350 roles into its digital operations and contact centres.
Up to 65 retail management roles could be disestablished.
IAG spokesman Kevin Hughes said customers had growing expectations for digital services.
"Covid-19 has accelerated many trends within the insurance industry and in the broader operating environment," he said.
"We know our stores have been a part of their local communities for many years, so the proposal to close them has not been taken lightly."
Waitaki Mayor Gary Kircher said the news was disappointing for Oamaru.
"A lot of people like the personal experience of going into the store," he said.
"My thoughts go out to the staff."
If staff were redeployed, he hoped they could remain in the district.
Otago Chamber of Commerce chief executive Dougal McGowan said new ways of doing business had emerged from the lockdown but people often still preferred one-on-one help.
"Many people do want face-to-face interaction."
Queenstown Mayor Jim Boult said the announcement was regrettable.
"All businesses are under stress at the present point."
Mr Hughes said a customer care team which had been established temporarily as part of the company’s Covid-19 response would be made a permanent service.
"For several years, we’ve seen a decline in visits to our retail stores as customers increasingly look to engage with us over the phone, via email and through our online platforms and digital channels," he said.
"Customers expect more digitally, and we are focused on delivering that for them."
Clutha-Southland MP Hamish Walker said he was disappointed for the Gore and Queenstown communities.
"It is a sign that the effects of the Covid-19 lockdown will continue for some time and there will be a long tail," he said.
"It again reminds us the focus needs to be on jobs and getting the economy up and running again."