Cleveland Federal Reserve President Beth Hammack on Monday said the U.S. central bank faces challenges as it attempts to balance fighting stubborn inflation or protecting jobs.

"On the inflation side right now, I continue to be worried about where we are from an inflation perspective," Hammack told CNBC's " Squawk Box Europe ."

"We have been missing our mandate on the inflation side, our objective of 2%, for more than 4½ years and I continue to see that we have pressure in inflation both in the headline, in the core, and particularly, where I am worried about it, is I'm seeing it in the services," she added.

Asked whether it is mistake for the Federal Reserve to be cutting interest rates given the economic backdrop, Hammack described it as "a challenging time for monetary policy," say

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