Mr Costello, who is chairman of the Future Fund, also hosed down claims by the lenders that the levy could undermine financial stability measures.

Speaking in Melbourne on Tuesday, he said banks would move to protect their shareholders and pass on the levy to customers.

"If I know the Australian banks, the Australian banks will do everything within their power to get this back out of their customers, not out of their shareholders. That's what they generally do," he said.

"I'm sure that the banks ??? will be working on plans to get it out of their customers."

Banks are furious they have been given only days to consult on the levy, and claim it could have unintended consequences for the financial system.

ANZ Bank chief executive Shayne Elliott said on Monday that the levy would directly impact its shareholders, many of whom were retirees who "rely on those dividends for their livelihoods".

Westpac chairman Lindsay Maxsted has called the tax "unbelievably bad policy" that would hurt shareholders and make the banks less strong.

In submissions to Treasury on Monday, banks argued the budget's levy would work against lenders' efforts to build up more liquid, or easy-to-sell, assets, designed to help banks cope through a period of turmoil.

In response to the banks, Treasury Secretary John Fraser on Tuesday said the tax was developed in line with "normal budget processes."

"Through those processes, careful consideration was given to the design of the levy, the costings and to its effect on the economy as well as the financial sector," Mr Fraser said in a letter to Australian Bankers' Association chief Anna Bligh.

"This consideration drew on Australia's experience with and development of financial sector levies over a number of years and international experience."

Mr Costello said the banks were big enough and profitable enough to handle the tax without it affecting financial stability measures.

"The Australian banks are very strong. I don't think we have to worry about them in the immediate future," he said.

The Future Fund, Australia's sovereign wealth fund, invests in Australian shares, including bank shares, on behalf of Australian public servants.

Some of Australia's largest super funds have also moved to play down claims that the levy would have an impact on investor returns.

Industry super fund Cbus, which manages $38 billion on behalf of 742,000 members, said the levy would not impact its decision to invest in the big banks.

"Any cost or levy on a bank does make the business harder to manage, but it hasn't materially affected the way we think about the banks and our portfolio," chief investment officer Kristian Fok said.

"It's not really in the governments,' or anyone's, interest for [the banks] to be weak."

AustralianSuper, which has 2.2 million members and manages more than $110 billion in funds, said the banks ultimately remained the "big beneficiaries" of the regulatory regime.

"They are in a privileged position and the public is dissatisfied. If you are in a privileged position, you have got to respect that," chief investment officer Mark Delaney said.

"The banks need to win back public support. There are a many things going on that affect returns."

CBA, ANZ Bank, National Australia Bank, Westpac and Macquarie Group were notified about the government's plan for a levy on their clients' deposits only an hour before the federal budget was handed down on May 9.

The legislation to establish the new banks tax is due to be released on Wednesday. A spokesman for Scott Morrison said the Treasury was consulting with the banks over the laws and "it is anticipated the legislation will be introduced within the next sitting fortnight" which begins May 22.

Prime Minister Malcolm Turnbull on Tuesday hit back at former Treasury boss turned NAB chairman Ken Henry, after he criticised the levy's design.

"He knows as well as I do that the banks can well afford to pay this," Mr Turnbull said.

Mr Morrison said it was "hardly a surprising headline" that the boss of a major bank wanted to pay less tax.

The government has indicated it was likely the Senate would hold an inquiry into the proposed laws.

Labor leader Bill Shorten has indicated his party would back an inquiry, but the opposition will vote for the proposed tax.

Meanwhile, Fitch Ratings' head of Australia and New Zealand financial institutions, Tim Roche, said the levy had triggered concerns the government would ratchet up the rate of the tax in the future.

If that occurred, it could prompt the banks to take on more risk to sustain their returns, or it could pressure some customers by leading to interest rate hikes.

Mr Roche estimated the bank tax would account for about 5 per cent of after-tax profits, but it would not shift the banks' credit ratings in its own right.

"We think that is a credit negative, but it's a mild credit negative," Mr Roche said at a conference in Sydney.

"Our bigger concern is that this becomes something that gets continually tweaked down the line. So you get a year down the road, and the government decides for whatever reason they want to make it 10 basis points, then another year down the road, it becomes 15 [basis points]. There is a risk that this continues through."

"The more that that comes through, the greater pressure it puts on the banks potentially needing to do things like going down the risk curve to maintain profitability, potentially passing through higher interest rate costs to borrowers, which would lead to, at the margin, greater levels of stress for those borrowers."

Mr Morrison has said the government has "no plans" to raise the levy's rate from 0.06 percentage points of non government-guaranteed liabilities.

The government has argued the tax is a small share of the big bank's $30 billion in annual profits, that the measure will enhance competition, and that many other countries such as the United Kingdom have bank taxes.

In the UK, the levy's rate has been changed nine times since it was introduced in 2011.

Tax Institute's senior tax counsel Bob Deutsch said the start date of the levy should be postponed to allow the banks time to get their systems in order.

"There are a myriad of unresolved issues most particularly around the methodology for calculating liabilities to which the 0.06 percent levy will apply," he said.

with James Massola and Nassim Khadem