(Reuters) - The Federal Reserve has further to go on raising interest rates as inflation has not even peaked yet, Cleveland Fed President Loretta Mester said on Tuesday.

We have more work to do because we have not seen that turn in inflation, Mester said in an interview with the Washington Post. It's got to be a sustained several months of evidence that inflation has first peaked - we haven't even seen that yet - and that it's moving down.

Other Fed policymakers on Tuesday also signaled they and their colleagues remained resolute and completely united on getting U.S. interest rates up to a level that will more significantly curb economic activity and put a dent in the highest inflation since the 1980s.

The U.S. central bank last week raised its benchmark overnight interest rate by three-quarters of a percentage point for a second straight meeting, with Fed Chair Jerome Powell indicating another unusually large rate hike may be appropriate again in September if inflation is not easing to a sufficient degree.

(Reporting by Lindsay Dunsmuir; Editing by Jonathan Oatis and Paul Simao)