Kashkari added in a television interview on Sunday that he is not sure whether the Fed has finished raising interest rates, and that monetary policy makers will use the data to form their opinions in this regard when they meet in September.
The US central bank raised interest rates by a quarter of a percentage point on Wednesday, to their highest level in 16 years, attributing this to continued high inflation.
The bank set the main overnight rate at a range of 5.25 to 5.5 percent.
The statement accompanying the announcement left the door open for another increase.
The US Federal Reserve aims to reduce the inflation rate to 2 percent.
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