Sheila Bair, former chairman of the Federal Deposit Insurance Corp., said the $2.5 trillion money- market mutual fund industry poses a potential risk to the financial system and the U.S Securities and Exchange Commission should take responsibility for regulating it.

“It’s not stable” and the industry is “a systemic risk,” Bair told reporters Sunday at a conference in New York organized by the National Association for Business Economics. “The SEC is responsible, and they haven’t moved forward.”

SEC Chairman Mary Schapiro in August gave up on a plan to tighten regulation of the funds, an alternative to bank accounts for individuals and companies, after three of five commissioners told her they wouldn’t vote to issue it for public comment. Treasury Secretary Timothy F. Geithner urged “further reform” of money-market funds in a letter last month to the Financial Stability Oversight Council, a group of regulators that includes the SEC and is headed by the Treasury.

The FSOC “should step in to act” if the SEC doesn’t, she told reporters. Bair, 58, is now a senior adviser to the Washington-based Pew Charitable Trusts.

The regulatory overhaul process “shines as a very bad example” of the industry’s confrontations with regulators, who are “still are trying to deal with a very obvious problem” that destabilized the financial system in 2008, Bair said in response to an audience question after a speech.

“It needs to be fixed,” Bair told economists. “What happens is a process, which is still ongoing, which makes everyone look bad, and I think that feeds into public cynicism.”