NEW YORK (Reuters) - The Securities and Exchange Commission should play a bigger role in regulating the market for U.S. Treasuries, the head of the SEC said on Monday in what appeared to be a push for a bigger role for her agency in a market largely overseen by the Federal Reserve and Treasury Department.

"I believe our regulation of the equity markets can and should be deployed to strengthen the U.S. Treasury market," SEC Chair Mary Jo White said in prepared remarks to a conference on the health of the government bond market, at the New York Fed.

"The controls we put in place around trading practices in many cases should apply to U.S. Treasury securities as well as equities, especially where those practices can threaten to destabilize markets or hurt investors," she said.

The Fed and the Treasury in recent years have dealt with the same sort of abrupt price dislocations experienced in years past in the smaller but more electronic stock market, which is overseen by the SEC.

White cited in particular firms that do short-term electronic "market making," suggesting that if they are trading in both the equity and Treasury markets they should be registered as dealers in both.

"A firm engaged in the business of buying and selling securities for its own account should be registered as a dealer, whatever type of securities it deals in," she said.

"I have recently directed the SEC staff to develop recommendations for the Commission to consider applying measures would further enhance our regulation of platforms that trade government securities."

(Reporting by Jonathan Spicer; Editing by Chizu Nomiyama)