Investors in money market funds “have been given a false sense of security,” and the industry needs more regulation because it is “working without a net,” the head of the Securities and Exchange Commission said Friday.

Chairman Mary L. Schapiro made clear that she plans to press for new rules despite what she called “the hue and cry being raised by the industry” against additional regulations.

“It’s time for us to take the next step,” Schapiro said, addressing a conference of securities lawyers in Washington held by the Practising Law Institute.

“To the extent that there’s a deadline,” she said, “it’s the pressure that we should feel from living on borrowed time.”

Many investors put savings into money market mutual funds seeking safety and ready access to their money. The funds play a crucial role in the economy by lending to corporations, often on an overnight basis, to finance routine operations.

Unlike other types of mutual funds, whose shares fluctuate in price based on the changing value of their investments, money market funds try to keep their share price constant at $1.

When a major money market fund called the Primary Reserve Fund fell below that share price at the height of the financial crisis in 2008-- called “breaking the buck” -- it set off a run on money markets that was so serious that the government stepped in to guarantee the multitrillion-dollar industry, Schapiro noted Friday.

But if that type of crisis were to happen again, Schapiro said, the government would not have the same tools at its disposal.

“Funds remain vulnerable to the reality that a single money market fund breaking the buck could trigger a broad and destabilizing run,” Schapiro said.

The SEC is considering making the share price a floating value, so that investors would have no illusion that the money market investment is risk-free. As an alternative, the SEC is considering a package of steps, such as requiring funds to maintain capital reserves and imposing fees or limits on withdrawals, Schapiro said.

That means that, in a crunch, the funds’ investors would not necessarily be able to withdraw all of their money at once. They might be forced to wait, say, 30 days to get the last one to five percent of their investment.

The Investment Company Institute, which represents the fund industry, says the SEC’s push for stricter rules is unwarranted. Schapiro’s assertion that the money market funds are susceptible to harmful runs is “a very contentious and debatable statement,” said Mike McNamee, a spokesman for the group.

The actions that the agency is considering to strengthen regulation of the money market industry would drive funds out of business, the group said in a recent statement.