"We are assessing the extent to which specific elements of the computer-driven trading environment may be working against investors rather than for them," White said.
Among the proposed measures is a rule intended to curb aggressive short-term tactics when the market is especially volatile. White also wants to see private high-frequency traders registered as dealers, a change that would bring them under SEC oversight.
White's proposals come amid mounting debate about the effect of superfast computers and algorithms, which now account for most 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," in which a computer problem sent stocks down wildly.
White expressed concerns about transparency and directed particular aim at "dark trading venues," which now account for up to 35% 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.
Although 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."