(Reuters) - San Francisco Federal Reserve Bank President Mary Daly on Thursday said that recent cooler inflation readings are a "relief" and she expects further easing in both price pressures and the labor market to warrant interest rate cuts.

"With the information we have received today, which includes data on employment, inflation, GDP growth, and the outlook for the economy, I see it as likely that policy adjustments, some policy adjustments, will be warranted," Daly said in a group interview held by phone. With the inflation likely to cool further, though with potentially "bumpy" progress, "one or two" interest rate cuts this year as projected in the June Fed policymaker forecasts could be appropriate, she said.

The Fed has kept its policy rate in the 5.25%-5.5% range since last July in an effort to cool inflation that had peaked at 9.1% a year earlier.

Daly spoke hours after a government report showed inflation cooling more than expected, and less than a week after other data showed a slowdown in monthly job gains and a rise in the unemployment rate to 4.1%. Both reports appear to add to the case for the Fed to start cutting interest rates sooner rather than later.

The consumer price index slid 0.1% last month after being unchanged in May, the Labor Department's Bureau of Labor Statistics said earlier on Thursday. It was the weakest monthly reading since May of 2020, early in the pandemic, while the 3% year-over-year rise was the lowest reading in a year.