The big banks are arming themselves for a propaganda war against the Treasurer’s $6.2 billion bank levy, with bankers warning that customers and shareholders will be the ones who pay the new levy.

To help pay for Tuesday’s cash-splash budget, Treasurer Scott Morrison announced a roughly $1.5 billion a year tax on the ‘Big Five’: CBA, ANZ, Westpac, NAB and Macquarie, to be paid over the next four years.

The banks are fuming, according to the industry’s peak lobbyist, and have been left no option but to extract more money from shareholders, savers, borrowers – or all three.

In a blistering press conference, Australian Bankers Association CEO Anna Bligh accused the Treasurer of a “grab for cash to fill a budget black hole” and of setting a “very dangerous” policy precedent.

Minutes earlier, there were reports that Commonwealth Bank CEO Ian Narev had sent an email to staff warning the costs could hit customers and shareholders.

The rhetoric is only hours old, but is already mirroring the fightback of big mining companies against Kevin Rudd’s Minerals Resource Rent Tax in 2009, which the industry branded a “super profits tax”. The Abbott government later repealed the tax.

Ms Bligh said the government had put the economy at risk by “singling out” its most profitable sector, simply because the banks were “easy targets”.

“Right now the major banks of Australia are very angry,” she said.

“There are only three options for the banks. It will be either be paid by shareholders, by savers, by borrowers or a combination of all three.

“I don’t think the Treasurer has thought through the full implications of this tax.”

Because bank share prices fell quickly and heavily on budget day, there has been speculation of a leak. Mr Morrison told the press gallery he had seen “no evidence” of this.

National Australia Bank CEO Andrew Thorburn echoed the lobbyists’ threats, saying the “tax” would impact “millions” of Australians, including every one of his bank’s 10 million deposits and borrowers and its 570,000 direct shareholders

“It is not just a tax on a bank. It is a tax on every Australian who benefits from, and is part of, our industry.”

But Mr Morrison cautioned the big banks, which make a combined profit of more than $30 billion, to simply accept the levy.

“Families absorb costs, small businesses absorb costs,” Mr Morrison told the National Press Club on Wednesday.

He said companies’ value lay in the way they treated their customers and the services they provided.

“They already don’t like you very much,” he said to the banks.

“But prove them wrong on this occasion. Don’t confirm their worst impressions. Tell them another story. Tell them you will pony up and help fix the budget.”

There are already suggestions the banks would soon raise mortgage rates by up to 0.15 per cent to recoup some of the costs of the levy.

Prime Minister Malcolm Turnbull also warned the banks that if they pass the cost on to customers, “the ACCC will be watching them very, very carefully”.

Between the levy’s introduction on July 1, 2017, and June 30, 2018, the consumer watchdog will be asking the banks to “explain” any increases to residential mortgage rates, fees and charges.

The levy is expected to reap the budget $6.2 billion in extra revenue over the next four years.

It will apply to banks with liabilities of more than $100 billion (indexed with nominal GDP), and will charge them a yearly sum equal to 0.06 per cent of the total value of those liabilities (which don’t include customer deposits).