White's proposals come amid mounting debate about the impact of superfast computers and algorithms, which now account for a majority of trading volume. The increasingly complex electronics systems that run stock trading have come under strain in recent years. They have resulted in incidents like the 2010 "flash crash," when a computer problem sent stocks down wildly.
White expressed concerns about transparency and directed particular aim at so-called "dark trading venues," which now account for up to 35 percent of trades. Unlike public stock exchanges, dark venues are private, off-market platforms that offer limited information about participants or how they operate.
White said the SEC will coordinate with the Financial Industry Regulatory Authority, the securities industry's self-policing organization, to expand disclosure requirements for such shops.
"Investors know very little about many trading venues that handle their orders," White said.
While the initiatives are likely to encounter resistance from high-speed trading firms and investors, White's proposals drew praise from some outside analysts.
"The time when the regulators waited to respond until a disaster has occurred has given way to following 'red flags' that showed potential problems," said Boston University law professor Tamar Frankel, an expert in securities law and financial system regulation. "This is a courageous and crucial approach by the Securities and Exchange Commission and its chairman."
White also said she wants to bolster market structures to help smaller companies, though she did not offer details. The number of domestic companies listed on U.S. exchanges has fallen by half since the 1990s, in large part because of fewer initial public offerings by small companies.
"If the downward trend continues, the strength of the U.S. equity markets can be compromised," she said.
White's proposals will be developed and refined by SEC staff in coming months before being considered by the full commission.