WASHINGTON (Reuters) - The U.S. central bank needs to proceed carefully as it decides when to begin cutting interest rates, Federal Reserve Governor Lisa Cook said on Monday, citing, as many of her colleagues have, the rough balance now between the dangers of easing monetary policy too soon and those of moving too slowly.

With inflation falling but still high, and the labor market still strong, "the risks to achieving our employment and inflation goals are moving into better balance," Cook said in remarks prepared for delivery to an event hosted by Harvard University. "Nonetheless, fully restoring price stability may take a cautious approach to easing monetary policy over time."

The path of lowering inflation back to the Fed's 2% target "has been bumpy and uneven," she said, "but a careful approach to further policy adjustments can ensure that inflation will return sustainably to 2 percent while striving to maintain the strong labor market," with the unemployment rate currently at 3.9%.

Cook's remarks did not indicate when she thinks an initial rate cut might be appropriate or the pace at which she thinks the Fed should proceed once it decides to lower its benchmark overnight interest rate.

Fed officials at a policy meeting last week projected at the median that three quarter-percentage-point cuts would be warranted this year, and investors broadly expect an initial reduction to happen in June.

Cook said she expects inflation to continue to ease for housing, a key part of price increases that have of late been declining slower than last year. The personal consumption expenditures price index excluding food and energy prices increased at a 2.8% annual rate in January, and in their most recent projections Fed officials saw that declining only to 2.6% by the end of this year.

Recent productivity gains could also allow the economy to continue to grow above trend without rekindling the high inflation seen in 2021 and 2022, Cook said.

Still, repeating what's become a touchstone phrase for central bankers trying to assure a "soft" economic landing from higher inflation, Cook said that "the risk of easing monetary policy too much or too soon is that it could allow above-target inflation to become entrenched and halt the progress that we have seen ... Easing too late could also do unnecessary harm by holding back the economy and depriving people of economic opportunities."