The Federal Reserve's third round of bond buying had a better than expected impact on the U.S. labor market, a Fed official said on Thursday, making it all the more necessary for the central bank to move faster with hiking interest rates.

St. Louis Fed President James Bullard pointed out that the economy has exceeded the economic forecasts the Fed presented in September 2012, when the central bank's latest bond buying program — known formally as Quantatative Easing (QE) — was launched.

"The policy rate normalization process remains far behind the schedule laid out at the launch of QE3," Bullard said in prepared remarks for a business event Thursday in Tupelo, Mississippi.

Bullard said raising rates in the first quarter of 2015, a forecast he has maintained throughout the year, would already be past what a standard monetary policy rule calls for. Bullard is not a voting member on the Fed's policy-setting committee.