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Prime Minister Scott Morrison says the decision about the ramifications for Westpac executives is in the hands of the board.Credit:Dominic Lorrimer

Mr Hartzer has apologised and on Wednesday said he was"utterly horrified"to learn of the detailed allegations potentially involving child exploitation. He hasvowed to personally lead an investigation to get to the bottom of the scandal,and signalled he does not intend to resign.

Asked if Mr Hartzer or someone else at the bank should resign over the scandal,Mr Morrison said it was a decision for the board and leaders of Westpac to make,rather than the government.

"These are things that the board and the management need to determine themselves,"Mr Morrison told ABC radio programAM.

"It’s not for the government to say who should be in those jobs or not,but they should be taking this very seriously,reflecting on it very deeply,and taking the appropriate decisions for the protection of people’s interests in Australia. These are some very disturbing,very disturbing transactions involving despicable behaviour."

The comments came as Westpac shares fell again on Thursday,with a decline of 1.8 per cent,to $25.20,in late afternoon trade.

AUSTRAC’s case against Westpac has put significant pressure on Mr Hartzer and the board,by claiming the breaches were the result of"systemic failures in[Westpac’s] control environment,indifference by senior management and inadequate oversight by the board."

Mr Hartzer on Wednesday said he accepted the case"almost overwhelmingly"but he rejected the claim of"indifference"on the part of the bank’s most senior leaders.

Bank analysts on Thursday warned the lender could face a fine as large as the record $700 million penalty imposed on Commonwealth Bank last year after its own money laundering compliance scandal.

Fund managers managing shares in the bank said Mr Hartzer would be under pressure,though they were divided about whether he would leave the bank over the affair.

Investors mutual investment director Anton Tagliaferro said he thought Mr Hartzer would probably make an"early exit,"as occurred with former CBA chief executive Ian Narev.

“As with Ian Narev it will probably just lead to an early exit,” Mr Tagliaferro said. “At the end of the day,someone has to be accountable. At the end of the day,the buck falls on the CEO and the board to some extent.”

In contrast,Atlas Funds Management chief investment officer Hugh Dive,a shareholder in the bank,noted the share price falls in Westpac since the lawsuit was served,but said Mr Hartzer had done well leading the bank overall.

"I would like to say he keeps his job because I think he has done it quite well,"Mr Dive said.