The Federal Reserve raised interest rates, and markets now price in up to two more hikes by year's end as inflation remains above the 2% target.

"So even if we strip out energy, ​which is really ​volatile, and strip out food ... inflation is still too high," Kashkari told Fox News.

The Fed now thinks inflation will take even longer to return to the goal, as stubborn inflation, rising rates, and economic uncertainty persist.

Chicago Fed President Austan Goolsbee (nonvoter) said that strong demand could also be driving inflation and that the Fed's job of lower the pace of price growth back down to the 2% goal may necessitate further rate increases that could negatively impact employment and economic growth.

Kansas City Fed President Jeffrey Schmid supported the Federal Open Market Committee's decision to raise the federal funds rate target range by 25 basis points to 3.75%-4.00% on Wednesday, he said on Friday.

Federal Reserve officials will decide whether to raise rates in the face of persistently strong inflation and bond market anxiety.

An expected Fed rate hike on Wednesday offered some relief to stock investors that the central bank was working to contain inflation.