In an extraordinarily blunt message from a federal treasurer, delivered during Mr Morrison's post-budget National Press Club address, Westpac, ANZ, NAB, Commonwealth and Macquarie Group were challenged not to pass on the cost of the tax, which will raise $6.2 billion.

Instead, Mr Morrison said, the banks should be mindful of their $30 billion annual profits and absorb the cost of the new levy - just as small businesses and families do with their rising costs.

The 0.06-percentage-point levy on money the big banks borrow to fund their lending excludes deposits of less than $250,000.

The banks have already started to fight back, warning that borrowers and shareholders could be forced to pay the cost of the tax, which could be passed on to customers.

And former prime minister John Howard has delivered a less-than-enthusiastic response to the budget, telling a PwC post-budget briefing in Melbourne he was "troubled" by powers given to a new Banking Executive Accountability regime by the Turnbull government, while arguing the document was created to pass a "recalcitrant" Senate.

The banking levy, he said, "was a tax on banks" that would be impossible for the Labor Party and the Greens to vote down.

His treasurer Peter Costello, at a separate budget briefing in Canberra, said the budget was politically smart and said the banking industry was "completely blind-sided by this, which shows how much influence they have in Canberra and how tapped in they are in Canberra".

The banks' warnings came as a surprised Labor Party indicated it would back the bank levy, which means it is certain to pass the Parliament.

Mr Morrison's message to the banks - families have to absorb costs, and so should the banks - will likely resonate with voters.

"The banks want to send a message to their customers about how much they value them? Don't do what they may be contemplating doing [raising rates or reducing returns]. Don't do it."

"They already don't like you very much. Prove them wrong. Don't confirm their worst impressions. Tell them another story. Tell them you will pony up and help fix the budget.

Mr Morrison also flagged personal income tax cuts to tackle bracket creep, which pushes taxpayers in to the next-highest tax rate as wages grow with inflation, in the next four years.

And he spoke at length about his brother-in-law, Garry Warren, who has multiple sclerosis, and his wife Michelle Warren, during the speech, as he outlined why the government had decided to raise the Medicare levy to fund the National Disability Insurance Scheme.

The decision to take on the five biggest banks and hit them with a new tax was a major surprise on budget night and is one of a number of measures that underscores a significant shift by the Turnbull government away from the austere policies of the Abbott-Hockey 2014 budget and towards new spending on infrastructure, health and schools.

Politically, the Turnbull government will be hoping the shift to the political centre will blunt Labor's attacks over fairness and equity, while arresting its slide in the polls.

Australian Bankers Association chief executive Anna Bligh said the banks would meet with Treasury officials on Thursday to receive more details and and added: "I don't believe the Treasurer has thought through the implications of this tax".

"Right now, the major banks of Australia are very angry; they feel they have had a tax imposed on them uniquely that does not apply to any other part of the business community," she said.

Westpac chief executive Brian Hartzer said the levy was a "stealth tax" that would reduce the international competitiveness of the sector, while flagging a possible increase in interest rates for borrowers, job cuts, or a reduction in returns to shareholders.

Commonwealth Bank chief executive Ian Narev said there had been a "lack of detail and the absence of any consultation" about the tax.

"However, as every business owner or employee knows, every extra cost needs to be borne by customers or shareholders, or a combination of both."

NAB chief Andrew Thorburn said the tax "cannot be absorbed".

"This tax is borne by these people. It is not possible to impose a tax without an impact on people," he said.

Deutsche Bank analysts estimated the impact on profitability of the five banks would be 3-6 per cent.

When news of the levy leaked on Tuesday ahead of the budget, investors wiped $14 billion from the value of banks stocks. Their share prices fell further on Wednesday.

with Clancy Yeates, AAP

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