Inflation has cooled in recent months as gasoline prices have retreated, but Federal Reserve Chairman Kevin Warsh said Friday that isn't enough to prove price growth trends are heading in the right direction.

In prepared remarks for his keynote address at the Jackson Hole Economic Policy Symposium, Warsh discussed his views on the current economic conditions. He noted that inflation has been durably above the central bank's 2% target for 65 months-despite some improvement in two key metrics, the personal consumption expenditures price index and the consumer price index.

"While this summer's PCE and CPI readings were better than expected, they do not tell me that underlying trends have meaningfully improved," Warsh said.

The tone of Friday's speech skewed more hawkish. Warsh, however, stopped short of acknowledging the Fed will need to intervene to get inflation all the way back to the current 2% benchmark-which the chairman reaffirmed is still the bank's target.

"Here is my standard: We must be confident that underlying inflation is moving to our objective, clearly and at sufficient speed. Otherwise, we have work to do. That's our job . . . our mandate . . . and our charge to keep," Warsh said.

Getting inflation down to 2% matters not just to markets, but to everyday Americans, he noted.

"If the Fed gets inflation wrong and judges the economy wrong, who gets the worst of it? Not the financial high-fliers," he said. "Hard-working Americans are the ones left to deal with inflation that is too high or jobs that suddenly appear less secure."

Overall, Warsh said Friday he was impressed by the overall performance of the U.S. economy, highlighting that there are recent signs it appears to have strengthened. Business capital expenditures are rising, consumer spending has been healthy, and expectations for corporate earnings growth remain "quite high," he said.

Additionally, Warsh sees the labor market as stable, calling out the unemployment rate at 4.1%-low by historical standards.

"Achieving both sides of our mandate over the medium term is not an either/or proposition. I do not believe that the Fed's dual mandate works at cross-purposes," Warsh said. He added that when labor supply is barely growing, it's natural that monthly job gains are going to be lower.

And while sectors such as housing and agriculture are showing strains, Warsh said he would be "hard-pressed to describe broad financial conditions as restrictive."