Act New Zealand leader David Seymour said the Budget increased taxes on those most in need.
The Taxpayers Union said the decision to hike taxes on smokers by 10% a year for the next four years was morally questionable.
But the Heart Foundation said ridding New Zealand's future of tobacco was vitally important.
"We would have preferred to see an increase greater than simply 10%, which has become the status quo.''
Associate Health Minister Sam Lotu-Liga and Maori Party co-leader Marama Fox announced the 10% rise for the next four years, saying raising the price of tobacco was the single most powerful tool to reduce smoking.
All smokers would face the price rises.
The more they smoked, the more they paid.
The more they paid, the greater the incentive to quit, they said.
About 15% of adult New Zealanders - or 50,000 people - smoked daily.
That increased to 35% for Maori and 22.4% for Pacific people.
It was estimated between 4000 and 5000 people died from smoking-related illnesses each year.
Increasing tax helped to reduce the incredibly serious harm caused by smoking, Mr Lotu-Liga said.
Mr Seymour said the Government had delivered a tax increase of $1200 to those households which needed a cut the most.
The average smoker smoked 10.6 cigarettes per day, taxed at 67c each, making $7.09 per day or $2588 a year.
The 10% tax increases for the next four years would increase the annual tax on an average smoker to $3786 per year, or $1198 per year in additional taxes per smoker under Budget 2016, he said.
The Government could have delivered a tax cut and made a bold and innovative health policy change by legalising e-cigarettes, to be sold without excise tax.
"Putting $3786 per year into smoking households by giving them an excise tax-free alternative to smoking would do more than any other poverty or public health initiative the Government is currently considering.''
Taxpayers Union executive director Jordan Williams said smokers already paid more than three times the health costs of their habit.
Penalising people for voluntarily choosing a damaging habit was morally questionable when the very people who paid were those who could least afford it.
Governments always needed more money and public health was a convenient excuse, he said.
Tobacco tax
• Tobacco tax to rise 10% a year for the next four years from January 1.
• The price of a standard pack will increase from about $20 to $30 in 2020.
• The changes are expected to generate an extra $425 million in tax revenue.
