Maori are living longer and their infant mortality rate will soon be the same as Pakeha.
But they are still over-represented in statistics of infectious diseases of poverty, partly because they live in overcrowded homes.
Read more from the Herald's Closing the Gaps series:
Closing gaps favours young
Figures from the Department of Statistics and the past four Censuses show Maori men now live on average five years longer than in the mid-1980s, the average lifespan growing to 72.4 years.
Maori women also have longer life expectancies, increasing four years over the same period to 76.5 years.
But both still lag behind Pakeha, who have made gains of their own, with men living an average of nine years longer and women six years longer.
Professor Tony Blakely of the Department of Public Health at Otago University's Wellington campus, said the infant mortality rate for Maori was continuing to fall while Europeans, Asians and others were perhaps stabilising.
In 1996, the Maori infant mortality rate was more than double that of Europeans, with 11.6 babies dying before reaching their first birthday.
By 2013 the rate had more than halved to 5.07.
Professor Blakely said the reasons included declining rates of sudden infant death syndrome or cot death, improving neonatal and early infant care and slow improvements in injury mortality.
His research showed non-Maori New Zealanders had the lowest infant and indeed child mortality rates in the OECD up to World War II, before falling behind other countries.
New Zealand is no longer the leader because of health inequalities, meaning its average mortality rate shifts up compared with a country with a more homogenous population.
While the infant mortality gap should be closed by the next generation, Maori children still suffer avoidable diseases, mainly because of poverty.
Professor Michael Baker of Otago University, Wellington, said Maori and Pacific Island families suffered infectious diseases at rates two to three times higher than Europeans.
He said evidence showed that the risk was not decided along ethnic lines but what people were earning.
"Most of the difference is explained by poverty - if you adjust for poverty you still see some residual differences by ethnicity but most of it goes away," he said.
Professor Baker said that over the past 20 years there was a pattern that coincided with benefit cuts and market rates for state homes, where the risk of hospitalisation rose for serious infectious diseases such as rheumatic fever.
For Maori and Pacific Islanders living in the most affluent neighbourhoods, the risk declined.
He said about 28 per cent of Maori children under 5 were exposed to household crowding in 2006 and 10.1 per cent were exposed to severe crowding where at least two further bedrooms were required to meet a family's needs.
For Pacific children the figures were even worse - 45.4 per cent lived in crowded homes and 20.6 per cent were exposed to severe crowding.
By contrast, only 8.2 per cent of European/Other children under 5 were exposed to household crowding and 1.9 per cent at the worst end.
"It is certainly a risk factor for a lot of serious diseases and young Maori and Pacific children are vastly more likely to be exposed to household crowding than other groups.
"Some of those infections are filling up our hospitals with children who probably shouldn't be there ... the problem is there are no available vaccines for most of these diseases and while that is the case there is a big social gradient."
Maori Party co-leader Tariana Turia said the improving trends for infant mortality and improved life expectancy were heartening. She believed that some of the change could be attributed to the Whanau Ora health initiative and the holistic approach being adopted by agencies and families around the country.
She was also pleased with the gains being made in reducing the uptake of smoking, with excise taxes and cessation support having an effect.
Mrs Turia said poverty was not the sole reason for poor health outcomes for Maori but "institutionalised racism" was also contributing to the inequalities between Maori, Pasifika and non-Maori.
"Research has shown that the persistent disparity in Maori health is due, at least in part, to behaviours on the part of their health care providers.
"For example, Maori receive fewer referrals, fewer diagnostic tests and less effective treatment plans from their doctors than non-Maori patients," she said.
"We must identify ways in which the health-care system can become more effective in addressing the health of Maori and Pasifika families.
"Poverty is not new to this generation. Poverty has been in our communities for decades and is not the sole reason for poor health outcomes for Maori. It is in fact institutionalised racism that is also contributing to the health inequalities between Maori, Pasifika and non-Maori."
To read more on this series and see our interactive graphics, click here.