UPDATE 1-Bank-taxing Australian PM challenges state bank levy

(Adds quotes from state premiers, bank shares)

SYDNEY, June 23 (Reuters) - Australian Prime Minister Malcolm Turnbull on Friday challenged a surprise decision by South Australia state to impose its own tax on banks, amid investor fears his federal government's bank levy could unleash a wave of new imposts on lenders.

Turnbull suggested South Australia's move, announced a month after the federal government angered the industry with its own A$6.2 billion ($4.68 billion) bank tax, could hamper investment and cost jobs in the state.

"When a state imposes higher business taxes within its own jurisdiction, is that going to drive investment, support, jobs within that state or is it in fact going to make it less competitive?" Turnbull told reporters.

South Australia announced a tax worth a combined A$370 million on five major lenders in its budget on Thursday, generating opposition from the industry which is still reeling form the tax imposed by Turnbull's conservative government in the federal budget last month. federal and state taxes would apply to the so-called "big four" banks - Australia and New Zealand Banking Group Ltd ANZ.AX , Commonwealth Bank of Australia CBA.AX , National Australia Bank Ltd NAB.AX and Westpac Banking Corp WBC.AX , plus investment bank Macquarie Group Ltd MQG.AX .

On Friday, shares of ANZ, Commonwealth Bank, National Australia Bank and Macquarie were down about 0.5 percent, in a slightly higher overall market, while Westpac was up 0.3 percent.

"Pandora's Box is officially open," UBS said in a research note. "As suspected the recent announcement of the Federal Bank Levy has already led to higher taxes on the banks."

Turnbull defended his federal tax as "national and consistent", rather than limited to one state.

South Australia Premier Jay Weatherill, of the centre-left Labor Party, told the Australian Broadcasting Corp banks were "not paying their fair share of tax" and the state's levy was "fair and proper".

South Australia's move has fired up speculation about whether other Australian states will follow suit, raising fears of an open season on bank taxes at a time when lenders are dealing with a cooling housing market.

Western Australia Treasurer Ben Wyatt said he was not considering its own bank tax but "we're watching South Australia and (seeing) how they're actually going to do it".

"I'm not going to pretend for a moment that it is not an attractive option," he added, speaking on ABC Radio.

A Victoria government spokesman said the country's second-biggest state had "no plans at this stage for anything like that".

A Queensland government spokesman said the state was not considering a bank tax, while a spokesman for the biggest state of New South Wales was not immediately available for comment. ($1 = 1.3261 Australian dollars)

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