(Reuters) - The U.S. Federal Reserve will be steadfast in raising interest rates to bring inflation running at four-decade highs back to the central bank's 2% target, St. Louis Fed President James Bullard said on Wednesday.

"We are going to be tough and get that to happen," Bullard said in an interview with broadcaster CNBC. "I think we can take robust action and get back to 2%."

Bullard, who also repeated his assertion on Tuesday the Fed will also probably have to keep rates "higher for longer" in order to gather enough evidence that inflation is coming down in a sustainable way.

"We're going to need to see convincing evidence across the board, headline and other measures of core inflation, all coming down convincingly before we'll be able to feel like we're doing enough."

Fed policymakers across the board on Tuesday signaled the central bank remains resolute 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 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 does not ease enough.

(Reporting by Lindsay Dunsmuir; Editing by Andrew Heavens and Chizu Nomiyama)