Civic Assurance chief executive Tim Sole refused to answer questions from The Star.
The delay has frustrated city council staff.
The city council's acting general manager corporate services Diane Brandish said: "We have clearly indicated our level of frustration to Civic. Ratepayers can be assured that we are not just sitting here just taking it."
She said although there was little the city council could do about the arbitration because it is between Civic Assurance and their re-insurers, staff were working hard to get through damage assessments.
"What we can do is keep getting resolution on as many damage assessments as possible so when Civic win their arbitration, and we have received independent advice that they have a strong case, there will be a whole pile ready to be paid," she said.
Ms Brandish said waiting three years for payment was unusual but the earthquakes were an "unprecedented event".
They were looking after claims for more than 1500 city council facilities, she said.
"If it had of been just one building which burnt down we would have been okay. Even if it had just been the September earthquake it would have been okay. But the February one was the single largest event."