RICHMOND, Virginia, Jan 11 (Reuters) - U.S. Federal Reserve officials said on Thursday that consumer price data for December did little to assure them that inflation is now on a steady track back to the central bank's 2% target, with more information needed before any decision to begin reducing rates.

Overall consumer price inflation on a 12-month basis rose to 3.4% in December from 3.1% the month before. But excluding volatile food and energy costs the pace of price increases fell to 3.9% from 4%, showing ongoing moderation in underlying price pressures.

It was an ambiguous outcome at a time when Fed officials are looking for some final but convincing bits of evidence that the pandemic-era spike in inflation has dissipated to the degree they can begin easing monetary policy and begin reducing the benchmark interest rate.

The December CPI report "just shows there is more work to do and that work is going to take restrictive monetary policy," Cleveland Fed President Loretta Mester said in an interview with Bloomberg TV.

"I think we need to see more evidence," before reducing interest rates, she said, with a March rate cut, currently anticipated by financial markets, "too early in my estimation."

In separate comments to reporters following a presentation at the Virginia Bankers Association, Richmond Fed President Thomas Barkin said the December inflation report was "about as expected," with prices rising slowly for goods but shelter and services costs still increasing at a more vigorous pace.

Barkin said that did not add to the sort of "conviction" about future declines in inflation that he feels he would need to begin reducing the Fed's target interest rate.

"This gap between services and shelter and goods is one that I am watching carefully because you would not want a goods deflationary cycle to end and find yourself disproportionately bearing the cost of shelter and services," Barkin said.

While noting the progress the Fed has seen in inflation this year, with some measures close to the central bank's 2% target over the past six months, "you'd have even more reassurance...if it were broader based" and included a slower pace of price increases for services and housing costs, Barkin said.

The Fed is expected to hold its policy rate steady at the upcoming Jan. 30-31 meeting, but financial markets anticipate rate cuts will begin in March. (Reporting by Howard Schneider and Lindsay Dunsmuir; Editing by Andrea Ricci)