Critics of the stable price, including former Fed Chairman Paul Volcker, have said this makes the funds more vulnerable to a run because small losses grow as a proportion of a fund's assets when investors withdraw, giving holders an incentive to redeem their shares before others.

Schapiro today described the $1 share price as "brittle."

The SEC's staff has also been examining at least two capital buffer plans. The proposals would require individual funds to create cushions for absorbing potential losses on investments. One plan outlined by university economists known as the Squam Lake Group would require that funds raise cash equal to 1 percent to 3 percent of assets by selling subordinated shares.

A separate plan floated by Boston-based Fidelity Investments in May would build buffers gradually over a number of years by withholding returns. Schapiro didn't comment on specific buffer proposals.

Capital Buffer

At a time of crisis, a capital buffer "could mitigate the incentive for investors to run since there would be dedicated resources to address any losses," she said.

The SEC enacted several rule changes for money funds in 2010. These created minimum liquidity levels for the first time, reduced the maximum allowed average maturity for fund holdings and introduced new disclosure requirements.

"The SEC's new money-market fund reforms were a critical first step," Schapiro said.

The need for additional steps to "bolster the resiliency" of the funds is "pretty unanimous among all the federal financial regulators," Schapiro said after her speech in an interview with television host Charlie Rose at the conference.

The SEC will make proposals "in very short order," Schapiro said in her speech, without giving a date. Any proposal would be followed by a public comment period.