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The stock market has transformed in the last decade into a place dominated by high-speed traders zapping orders to many exchanges, while regulators have been slow to react.

Now, the Securities and Exchange Commission is seeking to update the market’s rules for the new era.

The S.E.C. chairwoman, Mary Jo White, unveiled on Thursday a sweeping package of recommendations for new rules and other changes aimed at strengthening the structure of the market and improving disclosures for investors. The proposed changes would touch virtually every corner of the market, including exchanges, private trading venues, brokerage firms and high-frequency traders.

The proposals, outlined in a speech to a financial industry audience in New York, provide an answer to critics who have accused the S.E.C. of failing to do enough to curb market collapses and rein in lightning-fast traders. To many investors accustomed to only incremental changes in regulations, the proposals outlined in the speech were surprisingly detailed and comprehensive.

The speech also signaled that Ms. White, a former prosecutor who assumed the top job at the S.E.C. last year, plans to make market structure a top priority.

“Many market structure rules and industry practices were developed with manual markets in mind,” she said on Thursday at an exchange and brokerage conference sponsored by Sandler O’Neill & Partners. “They cannot be expected to optimally address all of today’s market practices.”

While Ms. White was careful to cite what she said were the benefits that electronic trading had brought to the market, including lower trading costs, she also forcefully criticized high-speed trading, which uses computer algorithms to place orders in milliseconds.

Saying she was focused on “aggressive, destabilizing trading strategies in vulnerable market conditions,” Ms. White proposed that the S.E.C. install additional safeguards against any harmful volatility in stock prices caused by rapid trading.

To improve the oversight of high-speed traders, Ms. White said she had asked the S.E.C. staff to draft a rule requiring such trading companies to register with the agency. She also is seeking to close a loophole that allows trading companies to avoid registering with the Financial Industry Regulatory Authority, Wall Street’s self-regulator, if they do their trading off traditional exchanges.

The recommendations aim to shine a light on the dark corners of the modern stock market.

Ms. White is seeking to develop a rule to improve the transparency of private trading venues, known as dark pools, by requiring them to release information about their operations to the public. She also said she wanted to work with Finra, the financial industry self-regulator, to expand a requirement that trading venues disclose information about trading volume.

Aspects of the market’s plumbing are also coming in for scrutiny. In some cases, brokerage firms serving institutional investors receive payments from exchanges for routing orders to them. Concerned about possible conflicts, Ms. White wants to make such arrangements more transparent.

Other recommendations address how exchanges distribute information and handle orders. Ms. White said that she would ask the exchanges to review the types of trading orders they receive and to “consider appropriate rule changes to help clarify the nature of their order types and how they interact with each other.”

Ms. White addressed a room full of exchange officials and other financial workers, including Robert Greifeld, the chief executive of the company that operates the Nasdaq stock exchange. Big exchanges like the Nasdaq are being scrutinized by Eric T. Schneiderman, the New York attorney general, for the services they sell to high-frequency traders.

In a statement on Thursday, Mr. Greifeld said he supported Ms. White’s proposals. “We believe they underscore the importance of maintaining an environment that supports transparency, simplicity and fairness across the capital markets,” he said.

But the proposals are likely to spur more heated debate as specific rules take shape. Ms. White recommended that the S.E.C. create a “market structure advisory committee” of outside specialists from different backgrounds to advise it on new rules. Any new rules face a long journey through the S.E.C., including a public comment period, before they can be put into effect. Adoption by the commission could take months or even years.

The recommendations are the culmination of many months of work by Ms. White and the commission. As high-speed trading has proliferated — it is now estimated to account for more than half of all shares traded in the United States — other investors have raised concerns about the safety and soundness of the markets.

Several malfunctions have intensified these concerns. In May 2010, in an incident known as the flash crash, suspect trades led the Dow Jones industrial average to plummet more than 700 points in minutes. Two years later, the S.E.C. adopted additional protections against market volatility, though they addressed only some aspects of the market risks. Ms. White, in her survey of Wall Street trading, has taken a hard look at the role of the S.E.C. in altering the market’s structure.

In 2007, the commission adopted a regulation that required stock orders to go to whatever exchange offered the lowest price. The change was intended to promote competition, but some investors have argued that it also introduced a potentially harmful element of complexity.

Ms. White recommended an examination of whether the regulation has led the market to become too fragmented across different trading venues.

One high-speed trader, Ari Rubenstein, the chief executive of Global Trading Systems, praised Ms. White’s speech for moving beyond “the misguided and misinformed accusations” about his industry that have proliferated recently.

Critics of high-speed trading found fuel in “Flash Boys,” a recent book by Michael Lewis, who contended on a book tour that the stock market was “rigged” against slower investors.

Ms. White appeared to dismiss that claim in her speech.

“The current market structure is not fundamentally broken, let alone rigged,” she said, with a sardonic chuckle.