At least one Federal Reserve member doesn't think last week's jobs report is reason enough for the Fed to put its tapering plans on hold.

San Francisco Federal Reserve President John Williams said Monday that one month's job numbers won't make or break Fed policy, and said he felt the central bank will still begin to unwind its purchases of bonds and mortgage-backed securities later this year as planned.

"It's really important for us to not [read too much] into one month's data, whether strong or weak," Williams said at a press conference at the annual meeting of the National Association for Businesses Economics. "The latest data is consistent with forecasts of gradual improvement. I'm still 100% on board with Chairman Bernanke's timeline."

Fed Chairman Ben Bernanke has said the central bank will begin to "taper" its $85 billion a month in asset purchases as the labor market improves. He predicted that would be sometime toward the end of this year.

Investors have taken that to mean the Fed's September meeting, and have sent bond yields and mortgage rates soaring.

But last week's August jobs report showed hiring that was weaker than expected and labor force participation at a 35-year low, which caused some to second guess the September timing.

Related: To taper, or not to taper? Reactions are mixed

Williams did not comment on whether the Fed will take action at its meeting next week, but did say he expects the taper to be gradual, starting this year and ending in June of 2014. He predicted the Fed wouldn't likely start raising interest rates until the second half of 2015.

He is not currently a voting member of the Federal Reserve, which rotates the voting privileges of its regional bank presidents. He will be a voting member in 2015.

Williams succeeded Janet Yellen as president of the San Francisco Fed in 2011, when Yellen was elected to the Fed's Board of Governors, which has permanent voting rights.

She is currently the Fed's vice chair and, along with Larry Summers, is considered a top contender to succeed Bernanke when his term ends in early 2014.