"Forty per cent of all residential buildings had initial assessments completed by the end of May compared with 32 per cent in April and 19 per cent in March."
Insurers continued to focus on the most damaged areas and were making "pleasing" progress, with 57 per cent assessed in the upper South Island as of May, compared with 45 per cent in April, Grafton said.
"In terms of residential building settlements, 29% had been fully or partially settled by end of May compared with 21 per cent in April and 11 per cent in March."
The time between assessment and settlement offer for residential properties was typically between 4 and 12 weeks depending on complexity, he said.
For commercial claims, 62 per cent of all material damage claims had been fully or partially settled by the end of May, compared with 57 per cent in April and 44 per cent in March.
Over $278m of commercial material damage claims had been partially or fully settled, Grafton said.