June 14 (Reuters) - Federal Reserve Bank of Chicago President Austan Goolsbee on Friday said he was relieved after data this week showed inflation in May had cooled, but he would still like to see "more months" of similar data before cutting interest rates.

"Inflation was back down to levels that, if we got a lot of months like this, we would be feeling so much better," Goolsbee told the Iowa Farm Bureau Economic Summit in Ankeny, Iowa. Government data published on Wednesday showed that consumer prices did not rise at all from April to May.

The data, which marked the softest consumer inflation reading since July 2022, was released in the middle of the Fed's two-day policy meeting. "My feeling coming out of the meeting was a little bit relief," Goolsbee said.

The Fed on Wednesday

left its policy rate unchanged

in the 5.25%-5.5% range. Fed Chair Jerome Powell said any rate cuts would wait until the central bank gets more confident that inflation is headed toward the Fed's 2% goal, or sees unexpected deterioration in the labor market.

Over the last 18 months, Goolsbee said, "We've actually made a lot of progress getting the inflation rate down." He added, "We just got to see more progress" before cutting rates.

The Fed, he said, is also keeping an eye on the health of the economy, where signs of pain like loan delinquencies are rising but are not to levels that would be associated with a recession.

If inflation continues to ease and the Fed can cut rates, he said, the Fed may be able to avoid recession altogether. (Reporting by Ann Saphir; editing by Diane Craft and Leslie Adler)