Its 2016-17 budget is $16.1billion, and over four years it would receive $2.2 billion in extra funding.
The Southern District Health Board will receive an extra $32million in 2016-17.
The health sector is experiencing unprecedented demand from a growing and ageing population.
Vote Health as a whole would be $304 million short of what it needed, Dr Rosenberg said.
"The squeeze is going on all over the place in terms of being able to maintain levels of service that people need and expect.''
Dr Rosenberg told the Otago Daily Times.
Dr Rosenberg is a joint author of an article published in the New Zealand Medical Journal today that takes the Government to task over health funding.
Using international data, it concludes that claims about New Zealand's healthcare spending are based on a "misrepresentation''.
The article, which had input from the senior doctors' union, argues that New Zealand health spending is low compared with most other Organisation for Economic Co-operation and Development countries.
In his press release, Dr Coleman said DHBs would get an extra $400 million in 2016-17. He said elective surgery, boosted by $96 million over four years, was a priority.
"This funding boost is part of the continued effort to increase elective surgeries by an average of 4000 a year. As New Zealanders live longer, access to elective surgery is becoming more important than ever.''
The Southern District Health Board's $32 million increase boosted its annual funding to $884 million.
New Zealand Nurses Organisation president Grant Brookes said extra money for elective surgery was welcome, but he had concerns about how it would be spent.
"We need to see this going into supporting employment of nurse practitioners to undertake first specialist assessments.
"We would also like to see equitable access to elective surgery across the regions and an effective formula developed to see this happen.
"This extra funding will not help those who don't even make it on to a waiting list,'' Mr Brookes said.
Health
• Health receives $568 million of new spending, the biggest increase in seven years.
• $96 million for elective surgery (over four years).
• $124 million for Pharmac for new medicines (over four years).
• $42 million for "vulnerable groups'', including expansion of Healthy Homes Initiative.
• Southern DHB gets extra $32million in 2016-17.
