Chief executives of Commonwealth Bank, National Australia Bank, ANZ and Westpac all labelled Treasurer Scott Morrison's levy a "bank tax", with three of the four explicitly saying the cost will be passed on.
"It is not just a tax on a bank," NAB chief executive Andrew Thorburn said.
"It is a tax on every Australian who benefits from, and is part of, our industry."
Mr Thorburn said that includes NAB's shareholders, staff and 10 million customers - who, like those of all big four banks, have already borne the cost of additional regulation through higher rates on home loans.
"It is not possible to impose a tax without an impact on people," he said.
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Westpac's Brian Hartzer called the levy a "stealth tax" on an industry that already paid more tax than any other.
"The cost of any new tax is ultimately borne by shareholders, borrowers, depositors, and employees," Mr Hartzer said.
Australian Banking Association CEO, Anna Bligh, told the Sydney Morning Herald the banks would meet with Treasury officials on Thursday.
She says Australians will pay for the new levy on big banks regardless.
"The treasurer is prosecuting a view out there that somehow this can be absorbed by banks, no organisation can absorb a tax," Ms Bligh said on Wednesday morning.
"A tax has to be paid and it can only come from one of three places: it either comes from savers, or from borrowers or from shareholders."
The share prices of the big five banks fell by almost $14 billion on Monday after speculation there would be a new banking tax in Tuesday's budget.
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Ms Bligh said this was a big blow to shareholders and a result of the government's banking tax.
"The biggest shareholders in Australian banks are the superannuation funds of every Australian," she said.
"There are literally millions of individual Australian families who are direct shareholders in banks and many of those are retirees who rely on dividends for their income.
"Those people who are retirees living on dividend income effectively take a pay cut thanks to the treasurer."
Mr Morrison's budget slugged the big four plus Macquarie Group with a 0.06 per cent levy on their liabilities - which includes borrowings and deposits - starting from July 1 to raise $6.2 billion over four years.
The treasurer called the measure a "fair contribution" that would help competition and budget repair.
In his budget night speech he said it was "specifically not" a levy on ordinary bank customer deposit and mortgage accounts.
CBA's Ian Narev, however, said: "every extra cost needs to be borne by customers or shareholders, or a combination of both".
Mr Narev also echoed Australian Bankers' Association chief executive Anna Bligh's point that the move had been undertaken without consultation.
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ANZ chief executive Shayne Elliot said the bank tax is a tax on the millions of ordinary Australians who are bank shareholders and bank customers.
"This additional tax fails to recognise the banking sector is already the largest taxpayer in corporate Australia contributing $11.5 billion each year to government revenue," he said.
"While the banking industry has made itself an easy political target, the industry is taking action to significantly improve its relationship with customers and the community."
Macquarie Group, in a statement, also said the impact on its operations was unclear.
Deutsche analyst Andrew Triggs said the levy looked "unusually harsh" and could reduce cash profit at the majors by between three and six per cent.
"While such a levy has been put in place in other countries such as the UK, typically this was in the years soon after the financial crisis and in countries which required bank sector recapitalisations," Mr Triggs said in a note.
Patersons economic strategist Tony Farnham said the levy, which is forecast to deliver $1.6 billion in revenue in its first year, could push dividends lower.
Banks may also quickly raise loan rates to offset the expense, he said.
NAB chief economist Alan Oster said it was unclear how ratings agencies - whose assessments affect how cheaply and easily banks can raise funds - will view the levy.
Shares in all four big banks fell by more than two per cent when the market opened on Wednesday - compounding the previous day's drops of between 2.1 and 3.6 per cent - before bargain hunters swooped to limit the damage.
CBA shares briefly dropped below $80 for the first time since December before recovering to close at $81.73 - down 0.35 per cent for the day.
ANZ gained 0.8 per cent, NAB and Westpac each dropped 0.7 per cent and Macquarie Group fell 0.6 per cent.
