He said if those banks did not change quickly enough, or were not taking the FMA's concerns seriously, then the regulator's focus could switch from monitoring to enforcement.
"Once you're in enforcement then you're possibly in a public environment where you're pointing to particular institutions saying, 'These guys have not listened to the monitoring report and everything else we're doing'," Everett said.
He said enforcement could include banks having their licences restricted around certain financial products.
"You can do quite a lot with a licensed entity short of taking away a licence."
KiwiSaver funds under management have swelled to more than $23 billion since the scheme was introduced in 2007 and competition among the major banks for members is intense.
The FMA's seven-point strategic risk outlook identified the main priorities in terms of its regulatory efforts over the next two to three years.
A key focus area for the regulator is distribution models that exacerbate conflicts of interest, such as remuneration arrangements that result in conflicted advice around the sale of financial products.
"These remuneration arrangements may include certain volume-based incentives, up-front commissions and trail commissions," the FMA said.
"Within the managed funds sector, we will also focus on fee-driven behaviour that is likely to result in unfair investor or market outcomes."
Everett said the strategic risks partly reflected the regulator's mandate under the Financial Markets Conduct Act, which has progressively come into force this year.
"Firms and professionals within our mandate should anticipate us paying attention to the seven priorities over the next two to three years," he said.
"Also, representatives of the finance professions, including directors, auditors, legal counsel and financial advisers, can expect us to work with them constructively on these areas to improve outcomes and build confidence."
Focus areas
• Governance and culture.
• Conflicted conduct, such as remuneration arrangements that result in poor advice around financial products.
• Capital market growth and integrity.
• Sales and advisory services reflecting the best interests of investors and consumers.
• Investors having access to tools that help them make informed financial decisions.
• Ensuring frontline regulators, such as exchange operator NZX, are effective.
• The FMA maximising its own effectiveness and efficiency as a regulator.