Daniel Crennan resigned from the Australian Securities and Investments Commission on Monday morning.

"I had been intending to retire from my position in July 2021," Mr Crennan said in a statement.

"However, in the current circumstances, I have decided that it is in the best interests of ASIC for me to resign now. I have therefore tendered my resignation to the treasurer with immediate effect."

Treasurer Josh Frydenberg has accepted his resignation, which comes after the expense revelations came to light on Friday.

"The government thanks Mr Crennan for his service and the important work he has undertaken during his time as deputy chair," Mr Frydenberg told AAP.

Mr Crennan, the watchdog's chief enforcer, was asked to move from Melbourne to Sydney in October 2018.

ASIC agreed to pay his relocation costs which included a rental allowance.

Mr Crennan said he was told the payments were consistent with ASIC policy but later learned about concerns raised by the auditor-general.

"I requested that ASIC cease paying me the rental allowance. I also offered and agreed to repay the rental allowance ASIC had paid to me," Mr Crennan said.

The auditor-general has recommended an independent review be conducted into issues raised regarding relocation payments, including those given to Mr Crennan.

"That review will take some time," he said.

"In order to ensure that ASIC's important work is not disrupted, I will remain available to facilitate the orderly transfer of work to my successor."

ASIC chairman James Shipton has also stepped aside after it was revealed the organisation paid more than $118,000 for him to receive personal tax advice.

Mr Shipton has agreed to repay the money, which he received after relocating to Australia from the United States to run ASIC in 2018.

The independent review will also examine these costs.

Shadow treasurer Jim Chalmers queried why Mr Frydenberg waited more than a month to take action, given his office was informed of the expenses concerns in an email on September 15.

The email said the auditor-general would be further writing to the treasurer "regarding payments made to key management personnel".

Mr Frydenberg told parliament he had been advised by his department to await a detailed letter of advice from the auditor-general.

"I accepted that advice," Mr Frydenberg said.

"The auditor-general has raised important matters which the government is acting on."

Australian Associated Press