The amount of money being spent on health care for Auckland is dropping as the population grows and the problem is getting worse.
Auckland District Health Board chief executive Ailsa Claire made the revelation in a blog post telling staff they needed to "challenge the way we've 'always done things'."
"We continue to face a challenge as the gap between our funding and projected population widens. It means we have to do things differently, we have to be brave, get quicker at decision making and give each other permission to try some things out."
Health board member Doug Armstrong confirmed the problem, saying "ADHB is progressively falling behind".
He said the widening gap was believed to be a consequence of Auckland's rapidly growing population causing issues with the population-based funding formula used by the Government to work out how much money each health board should get.
While modest population projections have Auckland reaching 2.3 million people by 2043, the actual number could be higher. Last year, the city increased by 43,000 people.
ADHB receives about $2 billion a year to provide services to Auckland but also has to use its funding to develop and maintain services provided to patients across the country.
Green Party health spokesman Kevin Hague, who is a former health board chief executive, said there was a problem with the population-based funding formula which had the greatest impact on the smallest and largest DHBs.
Mr Hague said the efficiency drive was producing fewer savings as time went on.
Ministry spokesman John Hazeldine said Auckland was expected to get more funding this year. He said ADHB performed well across measures of healthcare delivery. All DHBs faced pressures from time to time, and had regular talks with the Ministry.
A spokeswoman for Health Minister Jonathan Coleman said he was not available. ADHB chairman Lester Levy did not respond to messages. Ms Claire was also unavailable.