Boston Fed President Eric Rosengren told CNBC on Tuesday that he'd like to see more improvement in the job market and in economic growth before considering whether to start tapering the central bank's massive bond-buying program.
"One of the considerations we have to have is how sustainable the improvement in labor markets is," said Rosengren, the third regional central bank head on "Squawk Box" in as many trading days.
"We've only been growing at 2.2 percent growth over the course of this [slow] recovery. It has meant that the improvement in employment and improvement in labor markets has been slower than I'd like to see."
The dovish Rosengren—a voting member at the Fed this year—said growth needs to be closer to 3 percent to get the kind of pickup in the labor market that's needed. He added that he expects to start seeing better economic data in the first quarter of 2014 with only a gradual rise in inflation.
One of the goals of the Fed is to make a distinction between the monetary tools at its disposal, such as the difference between asset purchases and interest rates, Rosengren said.
"Just because we decide at some point that we should reduce the amount of purchases that we make in long-term securities, doesn't necessarily mean we change when we raise the short-term rates." He expects the Fed funds rate to remain quite low for quite some time.
On Monday, St. Louis Fed President James Bullard—a centrist, and also a voting member this year—said the central bank's pace of $85-billion-a-month in bond buying, known as quantitative easing (QE), has been extremely robust but "very reasonable" when interest rates are near zero. He also said there's room on the near $4 trillion Fed balance sheet for more asset purchases.
(Read more: Fed's Bullard: $1 trillion a year QE pace 'torrid')
But Philadelphia Fed President Charles Plosser said in Friday's "Squawk Box" appearance that specific dollar limits should be put on the size of the balance sheet. Plosser, a hawk, will be a voting member at the Fed in 2014. He also said the Fed missed an opportunity by not starting to scale back QE at the September meeting, as many on Wall Street had expected.
(Read more: Missed taper chance in September: Fed's Plosser)
Central bank policymakers also took no action last month, and some speculate that it's more unlikely that they'll begin tapering at their final meeting of the year on Dec. 17 and 18, which will be followed by Ben Bernanke's last scheduled news conference as Fed chairman. Janet Yellen, vice chair at the Fed, has been chosen by President Barack Obama to succeed Bernanke for the top job. She's awaiting her confirmation hearing.
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Yellen has spearheaded the Fed's more transparent communications strategy, which has not always been viewed in the markets as clear enough.
"It's going to take a little trial and error to get the communication correct," Rosengren said—adding that no single individual should be blamed. "It has been a complicated policy."
"One of the challenges is we've not been in a situation where we've tried to exit from a large balance sheet before. And [improving] communications is very important part of that." He also stressed that any moves the Fed makes need to be economic data-dependent.
Meanwhile, U.S. stocks Tuesday come off two days of gains for November's first two trading days, as investors look ahead to Friday's delayed October jobs report. The S&P 500 has been up in 15 of the past 19 sessions, and it's now up 24 percent for the year.