The Federal Reserve will probably have to return to more "traditional" policy-making now that the U.S. jobless rate has fallen to 6.6 percent, so close to the U.S. central bank’s existing 6.5-percent threshold for considering an interest-rate rise, a top Fed official said on Wednesday.

St. Louis Fed President James Bullard, speaking on a panel at the New York Stock Exchange, said the Fed will have to adjust its so-called forward guidance on monetary policy. He expects the Fed to drop its economic thresholds and have to "make more qualitative judgments" on when to tighten policy.

The debate over what to do about the increasingly less relevant thresholds is growing within the central bank.

As it stands, the Fed has said it expects not to raise benchmark rates until well after the unemployment rate falls below 6.5 percent, especially if inflation remains below target. Joblessness has fallen to 6.6 percent last month from 7.9 percent a year earlier, a drop Bullard called "dramatic."

The thresholds "have done well but we’ll have to modify this going forward," Bullard, a centrist U.S. central banker who does not vote on policy this year, said at a European American Chamber of Commerce event.

He downplayed the idea of simply lowering the unemployment threshold to 6.0 percent or 5.5 percent, as Narayana Kocherlakota of the Minneapolis Fed has suggested.

Instead, Bullard said qualitative guidance on rates is the "natural thing to do" since it is how the Fed will make policy over coming decades, and it would allow the Fed to take into account "all encompassing" measures of the health of the labor market.

The idea accords with what new Fed Chair Janet Yellen said on Tuesday.

Testifying to U.S. lawmakers, Yellen stressed that broader measures, such as the number of part-time workers and the long-term unemployed, should be considered in assessing the overall labor market.

The Fed’s mandate is for maximum sustainable U.S. employment, and low and stable prices. Based on published projections, the Fed aims for an unemployment rate between 5.2 and 5.8 percent; it targets 2 percent inflation.