"Obviously over time we would like to have more and more above the minimum."
Insurance Council chief executive Tim Grafton said insurers would comply with whatever the bank required.
But he questioned the focus on independence and said the quality and experience of directors should be taken into account.
"Generally, insurers already have good governance structures. I think it's important to stress that independence of directors is one thing, but the quality and experience they bring is another arguably more important set of factors to bear in mind."
Grafton said the council would talk to the regulator about the issue.
Last week Peter Brady, who oversees insurance for the Reserve Bank, told a directors' forum that directors and senior management of insurance firms could expect to be held to account for meeting regulations. "Responsibility and accountability for prudently running an insurance business rests primarily with the insurer's board and senior management."
Brady told the forum that if companies breached the Insurance Prudential Supervision Act (IPSA) he expected to hear from them first.
"We expect insurers to inform us immediately when a compliance issue is identified.
"We will want sufficient information to be able to quickly establish whether the issue represents a serious prudential matter, an isolated incident, or is a symptom of a more fundamental weakness. We will also want to know what the insurer's plan is to rectify the breach."
Brady said its requests for information should be dealt with promptly and said the time for leniency was over. "In situations where the information we require is not forthcoming or we need independent input, we would use the powers in IPSA to obtain information or conduct investigations.
"With the three-year transition period to full licences now over, compliance breaches are being dealt with more stringently."
He also told the directors to expect to provide more financial reports in the future. "This is currently being scoped and we anticipate sharing our proposals with the industry sometime around the middle of 2014."
Brady said high-risk insurers and those with the most potential to affect the financial system would receive the greatest attention.