Southern Cross has had problems paying clients since it bought its prime competitor, Aetna Health, last year.
Clients of the country's largest health insurer have waited months for claims to be settled.
Mr Kensington said the company promised to pay standard claims within 15 working days.
"We are well below that rate now, with claims currently being processed within nine to 15 working days," he said.
Last Friday, claims were being cleared at a rate of nine days, but if there was an influx the number of days would slip back to 15.
The funds would reach most people through a payment into their bank accounts, but a few would be paid by cheque.
Mr Kensington said Southern Cross hired 60 extra staff in the past two months to clear the backlog.
A PricewaterhouseCoopers report on Southern Cross' financial position is expected to be released today.
* Have you received your claim refund from Southern Cross this week? How long have you been waiting? Email us at
newsdesk@herald.co.nz
nzherald.co.nz/southerncross