Fed's Kashkari says inflation is 'still too high' even after softer-than-expected PCE data, labor market is 'pretty good'

Minneapolis Federal Reserve President Neel Kashkari said Wednesday that price growth remained a concern despite the latest data coming in cooler than economists predicted.

"Inflation is still too high," Kashkari told CNBC's Steve Liesman in an exclusive one-one-one interview as part of a Council on Foreign Relations event in New York.

Kashkari's comments follow Wednesday morning's release of the August personal consumption expenditures price index, known as the Fed's preferred gauge of inflation . The core version of index, which strips out volatile food and energy prices, came in lower than economists forecasted at 3% on an annual basis.

"There are many different measures of inflation, but it's running at around a 3% rate," Kashkari said. "It's been elevated now for more than five years. I didn't think the inflation data today really changed that story for me very much."

Kashkari said other economic data released Wednesday on consumer spending and gross domestic product showed the economy is "resilient."

During a roundtable a few years ago, Kashkari said he heard from a labor union leader that inflation was "worse" than a recession for their members. He said that conversation has influenced how he views the trade-offs between stability in prices and employment.

The Fed this month issued its first interest rate hike in three years in an attempt to bat down higher-than-preferred price growth. The central bank also signaled that another increase could be on the horizon.

He said on Wednesday that the labor market looked "pretty good" but not "great." Management services firm ADP earlier in the day announced that private payrolls expanded more than economists predicted in September.