The U.S. jobless rate will fall below 6 percent and inflation looks likely to rise back to 2 percent later this year, putting the economy closer to normal than most realize, a top Federal Reserve official said on Thursday.

"You are basically going to be near normal on both dimensions basically later this year," St. Louis Fed President James Bullard, speaking in an interview on Fox Business Network. "That's shocking, and I don't think markets, and I'm not sure policymakers, have really digested that that's where we are."

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Bullard reiterated his belief that raising rates by the end of the first quarter in 2015 will be appropriate, based on his forecast that U.S. growth will register 3 percent for the next four quarters.

If data disappoint, he said, he will revise that forecast.

Later Thursday, Bullard spoke at the Council on Foreign Relations, saying that at the current 6.3 percent rate of unemployment, the United States is "way ahead of schedule" on its trajectory toward a normal labor market. He added that that Federal Reserve may be behind the curve if the unemployment rate drops faster than expected, but he is confident that it will act appropriately.

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Bullard also said that he believes the U.S. is no longer in a low-inflation environment, and that inflation will continue to tick higher and rise above 2 percent next year.

—By Reuters with CNBC