Of the 23,925 over-cap house claims, the council says 13,566 have been settled and a further 2894 have been resolved but not yet fully settled because repairs are still under contract, waiting for consents or in progress.
Another 5700 claims are "in resolution" pending design work or waiting for cash payments.
That leaves just 1775 over-cap house claims still being validated, waiting for offers or undecided.
"We expected a substantial ramp up in over cap settlements in 2014 and this was evidenced by private insurers settling about 1100 over cap claims each quarter which is a 50 per cent increase on the quarterly rate from the previous year," Mr Grafton said.
"We're very conscious of the substantial number of claims that EQC has had to deal with and these represent a tiny proportion of their total claims, but we also recognise the frustration of customers whose claims have just reached or are yet to get to their private insurer. We have had constructive discussions with EQC and they are working hard to provide us with more clarity and certainty about the claims that will go over cap in 2015.
"While there will be more over-cap settlements coming insurers' way in 2015, even at this quarterly settlement rate we're confident that the majority of over cap claims will be fully settled by the end of 2016 target.
"There are still some complications with claims involving multi-unit buildings, retaining walls and land issues, but private insurers are working in a concerted effort with EQC, CERA and local authorities to overcome the hurdles."