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RNZ reported this week that IAG, the parent company to AMI and State Insurance, was no longer accepting new customers for contents insurance in the capital.
However, the minister has now revealed it is also declining property insurance applications.
The company makes up almost half of the country's insurance market.
Dr Woods said IAG decided not to take on risk-based pricing. Pre-existing policies would not be affected at this stage.
"They're just not offering cover in the Wellington region, We're still in the position of seeking some more information from the insurers."
Dr Woods said there was still insurance available in Wellington.
"We had officials speak to a range of people including IAG today, to seek reassurances from other companies there weren't plans to change their position.
"We have had those reassurances there is still insurance available and there are no plans to change that situation at this stage."
Asked what this meant for the premiums, Dr Woods said some companies were going to use risk-based pricing.
"Always with insurance people will need to have to shop around. They need to see what premiums suits them, what level of risk they're willing to tolerate in terms of excess."
Tower Insurance last year confirmed customers in earthquake-prone areas would have to pay more under its risk-based pricing. In June last year the company said said about 2000 people - or less than 1 percent of customers - would be getting an increase of more than $2000 while 97 percent would have a small decrease in premiums of $50-$100.
'Ongoing review' of EQC Act
Dr Woods added there were a number of backstops through the EQC Act to offer people natural disaster cover.
"Natural disaster cover is linked to your house insurance policy, but there is a provision in the act that if you can supply evidence you are unable to secure private insurance in the market, you can get direct natural disaster cover through EQC."
Under EQC cover for contents, insurers would pay the first $20,000 before EQC cover would come in.
She said she would be pressing the insurance company on this in coming days.
"We removed contents cover from the EQC Act at the end of last year. We have submissions from the insurance industry saying they supported this move because their belief was the private market would be able to pick up that area of risk.
"I will certainly be asking some questions in that area."
She said there was an ongoing stage two review of the EQC Act.
"We have to look at the act and give it a lot of scrutiny and say, 'Is this modern? Is it fit for the future or fit for purpose?' "