However, Melissa Cantell, chief operating officer at IAG New Zealand, said the company would maintain a strong presence here.
"We have approximately 3500 people in our New Zealand team, and will maintain a strong presence in New Zealand as not every activity or function will make sense to move off-shore.
"It's important to us to be connected to our communities across New Zealand."
The company would not say how many of its 3500 roles would head off-shore.
Parry said the union was disappointed not only for the workers it represented but also by the company's broader programme of outsourcing and he warned of consequences.
"Outsourcing of this nature is bad for all parties concerned, except for (potentially) the short-term profitability of the business.
"The most immediately affected parties are the New Zealand workers and their families."
He said the company's customers could also suffer from poor-quality service, administrative delays and vulnerability of their private data in a jurisdiction that is substantially less regulated.
But Cantell moved to reassure the group's customers that their information would be secure.
"We can assure customers that we take their privacy seriously and our off-shore teams follow the same robust processes as our New Zealand-based teams."
She said IAG was facing a changing insurance market with rising costs and numbers of claims each year, including an unprecedented number of natural disasters and weather events.
"To ensure our long-term sustainability as a provider of insurance in New Zealand we need to keep premiums affordable for our customers.
"To do this we are looking across our business at the way we operate to reduce our costs and improve our service to customers – and having some activities performed off-shore is just one way we are doing this."
Cantell said the business was increasingly using digital channels so its customers could do business with it at a time and place that suited them.
Earlier this month IAG reported its first-half earnings in New Zealand had more than tripled to A$119 million ($128.5m) in the six months ended December 31 from A$36m a year earlier.
While gains in premiums helped, the insurer's earnings were largely bolstered by a 15 per cent drop in claims expense to A$507m with just A$17m claimed from natural peril events against an allowance of A$43m.
The year-earlier period, which included the Kaikoura earthquake, reported natural peril claim costs of A$123m, exceeding an allowance of A$32m.