Policymakers at the central bank this week began to flesh out their thinking on the likely path for U.S. interest rates, with several calling for restraint and suggesting a willingness to push the economy past full employment to ensure a robust recovery and vanquish deflation risks.

William Dudley, the head of the powerful New York Fed, who is normally aligned with thinking at the central bank's Washington board, was the first to make the case for running the economy "hot" as a way to revive sagging inflation.

His remarks were buttressed by calls for rate-hike patience from two of the Fed's foremost "doves" in what amounted to a strong push-back against vocal inflation hawks who want to start tightening monetary policy sooner rather than later.

"You want to make sure that when you do lift off, that you actually are successful, that you don't lift off and then it turns out that the economy weakens and you have to reverse course," Dudley said on Monday. "We need the economy to run a little hot for at least some period of time to push inflation back up to our objective."

The latest chorus offered a reminder that an influential bloc within the Fed would prefer to err on the side of a bit too much stimulus than a bit too little, and suggested the rate hike path the central bank will follow will kick off quite slowly.

Even those pushing for earlier rates rises have signaled support for a gradual course, further evidence the Fed's grand experiment to breath more life into the economy is far from over.

EYES ON INFLATION

Fueling the calls for patience is a recent dip in inflation against a shaky global economic backdrop. Fed officials, who target 2.0 percent inflation, worry a misstep tightening policy could upend the U.S. economic recovery and risk of the kind of stagnation that has haunted Europe for years and Japan for decades.

"I'm nervous that there's not as much upward momentum in inflation as I would like," Chicago Fed President Charles Evans said on Wednesday, echoing a sentiment voiced earlier in the week by Narayana Kocherlakota, the head of the Minneapolis Fed.

Atlanta Fed chief Dennis Lockhart, who is often viewed as a weathervane for Fed policy, on Thursday said soft demand and inflation meant conditions for a rate hike would likely not "ripen" until mid-2015 or later.

Market estimates of inflation in five years time reached their lowest level in more than a year this week, and the latest messages from the Fed have led investors to scale back bets on how aggressively the central bank may move rates higher.

The eurozone is already flirting with deflation, while China's economy, the world's second-largest, has proven surprisingly weak. Researchers from the Cleveland Fed on Wednesday pointed to waning global price pressures as an indication U.S. inflation would likely stay subdued.

Dudley said pushing the U.S. jobless rate below the level Fed officials think is sustainable over the long-run would be "the mechanism to actually push inflation back up."

"I think that the inflation data is going to take center stage in the months ahead," said Lou Brien, an analyst at Chicago trading firm DRW Trading.

Shifting global fortunes, and anticipation of a Fed tightening of monetary policy at a time when the European Central Bank is unleashing more stimulus, has driven the U.S. dollar up to four-year high against a basket of major currencies which could put a further brake on U.S. inflation.

Fed officials, who historically are reticent to comment on the greenback, have taken note, with Dudley and others saying that the dollar's value would figure in setting policy.

The flurry of comments shed further light on economic projections issued by the Fed last week that suggest the willingness to let the economy run "hot" may be widely shared. The projections show the jobless rate reaching 4.9 percent to 5.3 percent in late-2017, while the consensus for the sustainable rate is 5.2 percent to 5.5 percent.

The strategy has its detractors, including Kansas City Fed President Esther George, who wants the Fed to begin raising rates now, and Dallas Fed President Richard Fisher who said on Thursday he expects rates to rise "sooner rather than later."

Cleveland Fed chief Loretta Mester expressed skepticism that overshooting on employment would lift inflation. "I don't believe monetary policy works that way," she said on Tuesday.