Dudley suggested one way to know if the Fed will reduce its purchases is if the Fed's economic forecast gets back in line with the outlook in June when it first announced its expected timetable to wind down the current quantitative easing program. Under QE, the Fed buys treasuries and mortgage-backed securities in an effort to drive down long-term interest rates.
FOMC members, in their latest economic forecasts, reduced their growth projections for this year and next by about a quarter point or 25 basis points on average from June. They now see 3 percent growth in 2014. Fed officials also raised substantial new concerns about the potential effects of higher interest rates and the fiscal debate in Washington on the economy and the outlook.
"If the economy were behaving in a way aligned with the Fed's June forecast, then it's certainly likely that the Fed would begin to taper later this year," Dudley said. "But whether that's going to happen or not remains uncertain."
Dudley said the reason some were surprised by last week's decision is that "people jump to conclusions. I think we're trying to be very plain-spoken. We're trying to be very transparent, but sometimes people think that we're hinting at something." He did concede "it's hard to communicate if you're not exactly sure what you're going to do at the meeting."
(Read more: Fed also does no tapering to its verbose statements)
Several hawks on the FOMC—those who do not support the current easy monetary policy—have said publicly since the meeting that the Fed undermined its trust and credibility with markets in it surprise decision.
Dudley also said that the Fed's forward guidance—promises to keep rates low and policy easy well into the future—will likely outlast the expected departure of Fed Chairman Ben Bernanke and the appointment of a new chairman. "The market should have reasonable confidence in the forward guidance because the reality is the Federal Reserve is not just about the chair."
He said the selection of current Vice Chair Janet Yellen, who is thought to be the front-runner of the nomination by President Obama, would also mean little change in policy. "I've known Janet for many, many years. I'm a huge supporter. She's smart. She's tough. I think she'd be a very fine choice, if that's where the president decided to go."
—By CNBC's Steve Liesman. Follow him on Twitter: