Government ministers are considering whether to pick up the cost of future earthquakes in Christchurch, as insurers abandon the city.

The Waimakariri and Christchurch councils have been told their earthquake insurance cover won't be renewed after June 30.

That will leave them having to pay if assets such as AMI Stadium, the Town Hall, the convention centre, all council buildings and even underground infrastructure are further damaged.

In Christchurch's case, the above-ground assets it owns are worth $1.85 billion.

A spokesman for Earthquake Recovery Minister Gerry Brownlee said the insurance issue was set to be discussed at the weekly cabinet meeting today.

Advice on what cover Government would offer for future earthquakes was likely to be issued this afternoon, he said.

Civic Assurance chief executive Tim Sole today told Radio New Zealand reinsurers had been " very badly burned" by the Christchurch earthquakes, leading many to pull out of New Zealand altogether.

His company had paid $7.5 milion in reinsurance premiums last year, while the full insured cost of the quakes was now around $750 million, he said.

"We can only renew our policies if we know we can pay out claims. We cannot get reinsurance."

It was unlikely Christchurch City Council or Waimakariri District Council would be able to turn elsewhere for earthquake insurance, he said.

"They would struggle deeply to get cover and they could have to turn to Government to provide that cover."

Christchurch City Council's general manager corporate services, Paul Anderson, said the council was not sure what it would do.

"We're working with our brokers to continue to try and place insurance. It's a huge battle."

It wasn't sure at this stage whether it would be able to get insurance even if earthquake cover was excluded.

Waimakariri District Council wrote to the Government about the issue on Friday.

Manager of finance and business support, Jeff Millward said: "Our brokers have said we're 99.9 per cent sure to get insurance, but not for earthquakes."

That included anything to do with earthquakes, such as fire, tsunamis and volcanic eruptions.

"Therefore we have no option but to put a proposal to the Government and ask for some sort of cover until confidence is restored back into the market.

"At the end of the day, what do you do?"