Mr Crennan started with the Australian Securities and Investments Commission in early 2018, based in Melbourne, but in a statement published on Monday morning, Mr Crennan said by October of that year, he was asked to move to Sydney due to the high number of commissioners based in Melbourne.

"ASIC agreed to pay me a relocation package which included a rental allowance," he said. "I was told the payment of this allowance was consistent with ASIC policy."

The rental allowance of $750 a week added up to $70,000 from the regulator.

Mr Crennan said he was told in September and October of this year about the advice from the Australian National Audit Office raising concerns about the payments and at that point he requested the payments stop and offered to repay them.

He said he had intended to retire from the position in July next year, but had decided it was best to do so now.

The rental allowance payments to Mr Crennan are under investigation, as well as the payment of $118,000 for tax advice for ASIC's chair James Shipton as part of relocation costs from the United States to Australia.

Finance Minister Mathias Cormann told Senate estimates Mr Crennan had not been asked to resign.

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Labor MP Andrew Leigh, deputy chair of the House economics committee said the government should have known something wasn't right with Mr Crennan's pay over a year ago when it was reported he earned more than the Chief Justice of the High Court.

"This issue only came to light because of the Auditor General, whose budget is being cut by the Morrison Government," he said.

"The Treasurer has questions to answer about when he knew of the Auditor General's investigation, why he is taking over two months to inquire into the Shipton issue, and whether his cuts to the Auditor General's budget are aimed at deliberately stymieing investigations of this kind."