Southern Cross will reveal its annual result within days.
Last month it rebranded Ellenco Pet Insurance, which it bought in 2011, and is promoting schemes such as its healthcare for couples.
At the start of this year, Southern Cross introduced a health essentials policy to cover 75 per cent of the cost of GP consultations, dental and optical, physiotherapy, dietitian, acupuncture, chiropractor, osteopathy and remedial massage, up to limits specified in the policy.
Southern Cross says it covers 61 per cent of the New Zealand market but pays 72 per cent of the country's claims.
Nib New Zealand has about 12 per cent of the market.
"They're Australian and for-profit and they're a corporate, and we're a not-for-profit ... society," a Southern Cross representative said.
Last year, an increase in the number of claims cut the society's surplus from $38.9 million in the 2012 year to $22.1 million.
The society described this as within the budgeted range and chairman Graeme Hawkins said that for every $1 of premiums, 88.1c was returned to members in claims.
About 1.2 million New Zealanders have health insurance. and industry experts said nib had spent large amounts in an assault on the New Zealand market.
A director of InsuranceMarket in Howick, Bruce Patten, said Accuro was the third big medical insurer although three life insurance providers - Sovereign, One Path and Partners Life - also had medical policies.
"Nib has made a substantial investment in New Zealand with huge promotional and rebranding campaigns which include sponsoring the Black Caps and Auckland Blues Super Rugby with [brand ambassador] Benji Marshall," Patten said.
"Nib is taking on the very entrenched Southern Cross, which had the market pretty much sewn up."
Nib had written about 10,000 new policies in the past year, which he said showed it was making inroads into the Southern Cross business.
Nib bought Tower Medical Insurance in November 2012 for $80.6 million, which included $8.6 million in surplus capital.
As part of the agreement, Tower provided services to nib under a transitional services agreement, with a deadline to complete the operational and IT separation of the business by the end of last year.
Read nib's announcement here: