Regional Development Minister Shane Jones wants the banking sector to pay a levy of at least $100 million a year for their "extravagantly privileged position".
His comments follow a report by the Financial Markets Authority and the Reserve Bank, released yesterday, into the conduct and culture of 11 banks that operate in New Zealand.
While the report did not find the widespread systemic issues that plague Australia, it found that banks did not have good processes to manage poor staff conduct, and were slow to remove sales incentives that pushed staff to sell items such as personal loans and credit cards.
According to the Reserve Bank, ANZ, ASB, BNZ and Westpac made a combined $4.9 billion, after tax, in the year to December 31, 2017.
Despite that, Jones said the banks were still cutting services to the provinces.
"I have asked for them to go easy and maintain connectivity in the provinces and they say they can't afford to.
"That's what I describe as the Aussie Haka ... You ask the Aussies to shout you a drink, and they say 'I've got nothing in this pocket or that pocket' and they throw their hands up.
"Banking strategists in this country and overseas are conscious that New Zealand is one of the few developed countries that do not have a banking levy. Aussie banks pay it in their own country, but they get a free good in our country. Make them pay for it."
Australia has introduced a bank levy of 0.06 per cent on the liabilities of major banks, expected to raise about A$1.5b annually.
Jones said a levy of $100m a year for all of the banks in New Zealand should be a starting point.
"The $5b profit reflects the extravagantly privileged position the banks occupy in New Zealand.
"What should the size of the levy be? I'm hoping that's part of [Consumer Affairs and Commerce Minister] Kris Faafoi's work programme, but if he asks me, my opening bid is at least $100m a year."
Banks have been given until next March to come up with a plan to effectively get rid of sales incentives and other shortcomings.
The FMA and the Reserve Bank will also be watching the Australian Royal Commission into the financial services sector, expected to report in February, to see what regulatory or legislative action to recommend in New Zealand.
Faafoi said if the banks fail to come up with adequate self-regulating processes, the Government will step in.
Jones conceded there was "no clear evidence of villainy" from banks in New Zealand, but without the right processes for dealing with poor conduct, that possibility remained.
NZ First members voted for a remit in September for a $50m levy from the banking sector that would be used to keep banks open in small towns.
Prime Minister Jacinda Ardern delivered a stern warning to the banking sector yesterday, saying banks needed to "lift their game".
She stopped short of saying that banking customers were being ripped off, but she said banks needed to do better.
"There are clearly weaknesses within bank systems and processes that have resulted in some instances of poor conduct and, as a result, customers have been worse off. That isn't good enough."