Ansvar's Australia and NZ chief executive, Andrew Moon, said the scale of the damage was much greater for Ansvar relative to its business than for other insurers because of the number of stone buildings it insured.
The risk of future earthquakes and the prohibitive cost of reinsurance had forced the decision, Mr Moon told Interest.co.nz. "We just can't expose ourselves to the risk."
Several days ago, Earthquake Recovery Minister Gerry Brownlee accused the Insurance Council of scaremongering by claiming that New Zealanders may not be able to get earthquake coverage.
Mr Brownlee returned from Monaco last week expressing confidence that reinsurers would offer earthquake coverage once the aftershocks had settled.
He told Interest.co.nz he was confident the withdrawal of Ansvar and Swiss giant Zurich would not spread to other larger insurers.
"I'm not pessimistic. We're seeing an unfolding of positions. Some will come and some will go," he said.
"We've spoken to the five big reinsurers and we know there's capital. The issue is going to be the price."
Ansvar will continue to offer other types of insurance directly from its Australian branch. It insures around 40 per cent of NZ's churches, as well as many heritage buildings, rest homes and charity properties.
Customers with annual contracts will not be able to renew them for earthquake coverage once the policy matures.
Zurich announced this week that it, too, would stop writing new earthquake cover for areas outside of Auckland, Northland and Waikato, which means the most earthquake-prone areas of Wellington and Christchurch will no longer be covered.
"We are all experiencing challenges in our trading conditions following the Canterbury earthquakes and we face the need to actively manage our exposure to earthquake accumulation," Zurich's New Zealand general manager, Adrian Riminton, said in a note to brokers.
Insurance Council chief executive Chris Ryan said he was not overly concerned by the decisions by Ansvar and Zurich to remove and reduce earthquake coverage. He said they represented only a small part of the market and competitors were likely to fill the gaps created.
Industry figures show the combined premiums of Ansvar and Zurich make up 1.5 per cent of the $3.3 billion worth of insurance business written annually in NZ.