U.S. inflation is falling "well short" of target so the Federal Reserve should be cautious about raising interest rates any further until it is confident that prices are headed higher, an influential Fed policymaker said on Tuesday.

In a dovish speech in the face of months of weak inflation readings, Fed Governor Lael Brainard said the U.S. central bank should go so far as to make it clear it is comfortable pushing prices modestly above the Fed's 2-percent target.

"We should be cautious about tightening policy further until we are confident inflation is on track to achieve our target," Brainard, a permanent voter on monetary policy, said in a speech in New York.

"There is a high premium on guiding inflation back up to target so as to retain space to buffer adverse shocks with conventional policy," she added. "I believe it is important to be clear that we would be comfortable with inflation moving modestly above our target for a time."