By Ann Saphir

San Francisco Federal Reserve Bank President Mary Daly on Thursday said that with U.S. monetary policy "well into" restrictive territory, a lot of progress toward 2% inflation, and the recent rise in U.S. Treasury yields, the Fed may not need to raise rates any more.

"If we continue to see a cooling labor market and inflation heading back to our target, we can hold interest rates steady and let the effects of policy continue to work," Daly told the Economic Club of New York.

And with the rise in long-term rates in recent weeks, she said, "the need for us to take further action is diminished because financial markets are already moving into that direction and they've done the work."

Still, she said, "there are real risks" to inflation's march downward.

"If the deceleration of growth and inflation stall, activity begins to reaccelerate, or financial conditions reverse some of this tightening and loosen too much, well we can react to those data and raise rates further until we are confident that monetary policy is sufficiently restrictive to complete the job."

"We need to keep an open mind, and have optionality," Daly said.

(Reporting by Ann Saphir; Editing by Chizu Nomiyama and Andrea Ricci)