The high cost of super is a key focus of financial system inquiry chair David Murray, who observed in his interim report there was "little evidence of strong fee-based competition" and super costs were higher here than overseas.

The comments have sparked a fierce response from the powerful superannuation lobby, with funds arguing cost must be compared with performance.

But the latest submissions from the Australian Prudential Regulation Authority, Reserve Bank and Australian Securities and Investments Commission all say there remains scope for more competition in the retirement savings sector, notwithstanding some signs of improvement.

ASIC noted a "continued lack of fee-based competitive tension" in super, and it said this was influenced by the fact many members were uninterested in their super savings.

Funds often had opaque fee models and tended to compete on product features that were hard for consumers to compare, it said.

"Superannuation funds have sought to distinguish and compete on product and service propositions rather than  directly on fees," ASIC's submission said.

The Reserve Bank supported Mr Murray's "consideration of measures to enhance competition and reduce costs" in super. These could include more scrutiny of funds' back-office costs, and consideration of whether members were being exposed to more risk than they realised, it said. It also conceded that costs were not the only factor for investors to consider.

APRA, which regulates super funds, said it expected to see greater competition for default super funds as it published more information on how no-frills MySuper funds were performing.

"Publication of detailed product-level data, including fees charged, costs incurred and net return information, will significantly improve transparency in relation to MySuper products, in line with the objectives of the MySuper reforms. It is also expected to enhance competition," the regulator said.

Their support for increased competition between funds is likely to be influential given the inquiry's keen focus on how to make superannuation more efficient.

Yet it remains unclear what specific policies Mr Murray may recommend, after there was no support from the top regulatory agencies for going down the path of Chile and auctioning the right to be the nation's default fund, one option Mr Murrray has flagged.

Fees for default pension funds have plunged 65 per cent in Chile after it introduced a system where funds have to compete on costs to be the fund for members who do not make an active choice.

However, APRA was cool on the idea. Its submission says this option could "adversely affect member outcomes," and focusing too much on costs may mean trustees do not invest in growth assets. The RBA and ASIC did not comment on the proposal.

Against the push for more competition, the super industry has hit back by dismissing comparisons with overseas, as many countries overseas have very different retirement systems to Australia's.

AMP Capital cited figures showing returns over the 2000s in Australia were fifth best out of a group of 14 countries from the Organisation for Economic Cooperation and Development.  Moreover, it argued it could be misleading to only compare funds on costs, as investors needed to look at "risk-adjusted returns."

SuperRatings also said MySuper had caused the average fees for an account holding $50,000 to fall by almost a third to $513.

The regulators acknowledged there were some encouraging signs, saying Labor's MySuper scheme may already be dragging down super fees, but their comments suggest they think more could be done for members.

The top financial regulators were also united in their concern that direct gearing by super funds had introduced new risks into the financial system.