ANZ Bank chairman David Gonski is urging the government to enshrine in law its commitment not to raise the rate of the bank tax, in a concession lenders cannot stop the levy from going ahead.

Mr Gonski, also a key advisor to the Coalition government on education, broke his public silence on the tax on Thursday, but avoided the blunt attacks of other senior bankers.

Presenting the tax as a sign of the poor relationship between banks and the broader community, Mr Gonski said ANZ would push for amendments to limit the potential for future increases in the levy, a key fear of the banking industry.

The intervention from one of the country's most senior businessmen came as the banks' lobby group made a plea for more public scrutiny of the levy through a Senate inquiry, after a rushed period of industry consultation.

In a letter to ANZ shareholders, Mr Gonski said the bank was disappointed by the new tax, which he saw as further evidence of the breakdown between banks and the community.

He said the bank would lobby the government to ensure the levy was "fair and efficient," and it would push for the tax rate to be fixed in the legislation, so that it could not be raised without the agreement of the parliament. As currently planned, the tax will be an 0.06 per cent charge on bank borrowings, excluding most retail deposits. Analysts predict the government may raise the rate of the tax in the future.

"Clearly we are disappointed at the introduction of this new tax. However, given the support it has in parliament, we accept that it will pass into law," Mr Gonski said.

"Our focus has been to work constructively with government to ensure the legislation associated with [the] tax is as fair and efficient as possible in the circumstances."

Mr Gonski also said the tax should be scrapped once the federal budget was repaired; it should apply to foreign banks; and financial regulators should advise publicly on the impact of any future changes to the tax.

He argued ANZ was "working hard" to build community trust in banks, and said banks needed to "think and act differently" for this to occur.

"It is not in shareholders' interests or the national interest that the relationship between banks and the community continues in this way," Mr Gonski said.

The poor relationship between banks and the community was also picked up on by the chairman of the Australian Securities and Investments Commission, Greg Medcraft.

Speaking at a conference in Sydney, Mr Medcraft said bank moves to raise their interest rates independently of the Reserve Bank had eroded public trust in the industry.

"I've been very annoyed about the movement out of cycle, because I think that's where the breach of trust is," Mr Medcraft said at a Stockbrokers and Financial Advisers Association conference in Sydney.

"Australians have always, they've gone, 'they'll pretty well go up and down with movement in the cash rate,' that's where the problem has occurred, frankly."

A letter from Australian Bankers' Association chief executive Anna Bligh said banks had only 39 hours to comment on draft legislation, and pushed for a Senate inquiry and regulatory impact statement to be published.

"The ABA has concerns regarding the speed of introduction of legislation for the $6.2 billion levy on Australia's five largest banks, and believes that further consultation with banks and the public is necessary to avoid the risk that the levy will have unintended consequences for the Australian economy," Ms Bligh said.

The big four banks expect to pay $965 million combined in extra tax as a result of the levy and have protested that they were not consulted on the levy, which may end up being passed on to customers.

Westpac expects to take the heaviest blow at $260 million a year after tax, while NAB ($245 million), ANZ ($240 million) and CBA ($220 million) also outlined significant costs.