WASHINGTON, D.C. – Mary L. Schapiro said the Securities and Exchange Commission intends to directly “confront’’ a new round of long-term reforms to the nation’s money market mutual funds.

But she made no commitment to any of the options that the federal regulator of the funds business has been considering, whether it be allowing the net asset value of a money market fund to fluctuate from $1 a share, as the value of their assets move up or down, to setting aside capital buffers to protect against runs such as the one that occurred in September 2008.

The SEC remains committed to “honest open debate” on its proposals, awaited for months by the $2.6 trillion industry, she said in conversation with Mellody Hobson, president of Ariel Investments at the general membership meeting of the Investment Company Institute.

But she made no announcement of what the SEC plans to propose.

The ICI, the mutual fund industry’s leading trade group, has had a “rocky time” of late with the SEC over the money market reforms that are in the works, as ICI president Paul Schott Stevens would put it. Hobson, in starting discussion on the subject with Schapiro, noted that the industry and the SEC had been “at loggerheads” on how to proceed.

In March, ICI general counsel Karrie McMillan, had castigated the regulator’s plans for a second round of post-2008 reform of the industry. “What the SEC is considering doing to money market fund investors is outrageous,’’ she asserted at the 2012 ICI Mutual Funds and Investment Management Conference in Phoenix. “Outrageous.’’

“Outrageous” in the ICI view were a proposal being considered by the SEC that would allow the net asset value of a money market mutual fund float from a stable $1 a share; a proposal that would require capital buffers, and a proposal to slow the ability of investors to pull their money out of funds, even when there was not a run.

At that time, the SEC criticized the industry for conducting dialogue on the reform through the press. “That deeply disappoints me, the chairman, and the commission staff,’’ Commissioner Elisse Walter said. She told fund industry executives to re-engage with the SEC on a second round of reform.

In a first round of reforms of the money market industry, in 2010, the SEC tightened credit quality standards, shortened weighted average maturities, and for the first time imposed a liquidity requirement on money market funds.

That came in response to the crisis that erupted in September 2008, when the nation’s oldest money market fund, the Reserve Primary fund, infamously “broke the buck.”

The delineating feature of money market funds, as Schapiro would note, is that they seek to maintain a stable net asset value at all times of $1.00 per share. But, Reserve Primary was heavily invested in Lehman Brothers assets. When Lehman headed into bankruptcy, the value of those assets fell dramatically and the fund could not maintain the $1 net asset value of its shares.

Investors pulled $310 billion from money market funds, with large institutional investors making the biggest run on the bank, in effect.

The run was stemmed by federal intervention. The U.S. Treasury on Sept. 19, 2008, created a Temporary Money Market Fund Guarantee Program, that gave, for a time, assurances to investors that the balances in their accounts at money market funds were safe.

Unlike savings accounts at banks, money market funds are not protected by the Federal Deposit Insurance Corporation.

Schapiro said Friday that she was “counting on the industry to engage constructively in the debate” on what to do next.

The federal government cannot step in and rescue the industry the next time the buck gets broken, she noted. “The tools to do that do not exist any longer,’’ she said. “So we want to confront this issue.’’

She said she was “counting on the industry to engage constructively” in the debate on what to do next and applauded fund firms which have come in to talk with her “about these issues.” She said she had conversed with fund companies as recently as this week, on what to do.

The risk of a run “is real, it’s happened,’’ she said, “and it has to be resolved.’’