UPDATE 1-Fed should be cautious in face of weak U.S. inflation -Brainard

(Adds comments, policy context)

NEW YORK, Sept 5 (Reuters) - 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 clear it is comfortable pushing prices modestly above the Fed's 2-percent target.

Brainard, a permanent voter on the Fed's monetary policy who has in the past convinced colleagues to delay tightening, seized on a core price reading that has dipped to 1.4 percent and has remained below a 2-percent target for five years.

"We should be cautious about tightening policy further until we are confident inflation is on track to achieve our target," Brainard 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."

The Fed has raised rates twice this year and, according to estimates issued in June, expects to hike again before year end. Yet investors are skeptical and give a December rate hike about a 30 percent probability.

Brainard suggested she was prepared, however, to back the announcement of a reduction of the Fed's $4.5-trillion balance sheet at a mid-September policy meeting, as widely expected.

Yet she made the case for caution given the trend of depressed "underlying" inflation, and the lack of dangerous financial asset bubbles that would force the Fed to raise rates more quickly.

There are reasons to worry, she said, that rising employment will prove as reliable as in past cycles in boosting inflation. "It could take a considerable undershooting" of the equilibrium unemployment rate to do so, she said.

Addressing Hurricane Harvey last week, Brainard said it raises uncertainties for the economy for this year and will likely have a "notable" effect on growth in the third quarter, though that should be followed by a year-end rebound.

She added that, given predictions earlier this year for fiscal stimulus from the Trump administration and a more recent wave of downgrades to those expectations, she has revised her outlook in kind. (Reporting by Jonathan Spicer and Stephanie Kelly; Editing by Chizu Nomiyama)