A dozen top Federal Reserve officials pressed regulators Thursday to toughen a proposal that would revamp a portion of the nearly $3 trillion money-
market-fund industry, and called a key aspect of the plan “imprudent.”

The heads of the 12 regional Federal Reserve banks voiced their criticisms in a letter to the Securities and Exchange Commission, which has been struggling to tackle the industry’s vulnerabilities for years. In June, the agency released a plan that aimed to change how a segment of the industry operates.

Federal scrutiny came as a result of the problems that erupted in September 2008, when a major money-market fund “broke the buck” — meaning its value fell below $1 a share. A panic ensued, and investors withdrew $300 billion in a week, exacerbating the financial crisis. The government responded by temporarily guaranteeing that investors would be repaid, an option that’s no longer available because of a change in the law.

To prevent a repeat, the SEC proposed two plans that focused solely on “prime funds,” which invest in short-term corporate debt. One of the plans would allow the value of “institutional” prime funds to fluctuate, reflecting the true value of the underlying assets.

One share of a money-market fund is generally set at $1, so investors can get back the full dollar they put in. Critics say the arrangement has lulled investors into a false sense of security, creating an impetus for them to flee at the first sign of trouble.

The bank presidents agree with that assessment. They want the SEC to require a floating share price for retail prime funds, as well as institutional ones.

The SEC declined to comment. But the agency has said it narrowly tailored its initiative to affect only the segment of the money-market-fund industry that suffered the most severe disruptions during the crisis.

In their letter, the presidents said that approach was flawed. Some individual retail funds experienced withdrawals above the historical norms during the crisis or used money from their parent companies to shore up their funds, they said.

While retail investors did not flee “en masse” back then, “it seems imprudent to assume that their behavior in the future will be the same,” the letter said.

The bank presidents also criticized the second alternative proposed by the SEC, which would allow all prime funds — institutional and retail — to block withdrawals and impose fees on investors when fund assets fall below a certain level.

That approach “does not meaningfully reduce the risks” that money-market funds pose to financial stability,” the letter said.

The two options the SEC laid out in June could be adopted separately or in combination.

The letter is among many that the SEC has received in response to its proposal, which was unveiled shortly after SEC Chairman Mary Jo White joined the agency. The Federal Reserve’s board of governors has not taken a position on the SEC’s most recent proposal.