Little said the tribunal would enable homeowners to resolve longstanding residential insurance claims including with Southern Response or the Earthquake Commission, and would have the ability to award costs or general damages.
The Insurance Council said it had taken far too long for action to be taken.
"The tribunal won't be up and running until 2019, the best part of 18 months since the Government was elected. It will have been nearly nine years since the first quakes, far too long by anyone's measure to be finally trying to sort this out. Insurers want to settle their customers' claims as quickly as possible but we're still receiving, on average, two claims a day from EQC," Insurance Council chief executive Tim Grafton said.
The Insurance Council was also concerned that only policyholders would be able to bring cases, not insurers.
"This is unfair as it only deals with one half of the problem and the Ministry of Justice agrees, saying it creates inequity of access to justice.
"A tribunal that allowed both sides to bring claims would be fair and balanced and truly working towards the goal of helping everyone find resolutions and move forward from the quakes," Grafton said.
The Government's own agencies, EQC and Southern Response, accounted for the majority of outstanding claims but neither they nor private insurers were consulted on the bill before its introduction, he said.
The council also said it wanted certainty that the tribunal would respect the rules of natural justice and fair procedure, the need to apply the rules of evidence, to be bound by precedent, and the ability to appeal significant points of law.
"Any bill that does not respect these legal principles will not be supported by the insurance sector," Grafton said.
"The people of Canterbury deserve better than a tardy process that fails the test for best practice policy development."
Woods said the time for consultation was during the select committee process and the Insurance Council have a chance to voice its opinions then.
"The bill has been tabled, it will have its first reading and it will go through that process. I'm left wondering why the Insurance Council thinks they deserve special treatment," she said.
Woods said the tribunal would level the playing field.
"This is about giving people who have not had a way to get their claims settled. They haven't been able to afford to go through the courts. It's about giving claimants an alternative way through the system. The insurance industry can well afford to use the courts if that's what they need and there are other tribunals that are only claimant initiated," she said.