New York Federal Reserve President John Williams told CNBC on Friday that the central bank is listening "very carefully" to the market's concerns on growth, but believes the U.S. economy is in good shape.

Fed Chairman Jerome Powell and other central bank leaders are moving to more data dependency, Williams said, which includes listening to people in financial markets as well as local businesses.

"We are listening very carefully to what's happening in markets for two reasons. One is financial conditions have [an] important influence on [the] economic outlook," Williams said on "Squawk on the Street" in an interview with CNBC's Steve Liesman. "Second, I think we are hearing something important from markets, and that is a concern risk to the economy and potential further slowdown than we currently expect in our base case."

It's not just looking at the "hard GDP data" or "CPI data," he added. "We're listening to the message of the market."

Williams appeared on CNBC after the Fed on Wednesday raised its benchmark interest rate for a fourth time this year and lowered its rate hike projection for 2019 from three to two.

He said Friday that this week's rate increase was "fully justified and makes sense," but he added the Fed is open to reconsidering its views on rate hikes next year. Stocks rose sharply during Friday's interview, but then faded.

Powell did leave the door open to other options next year, emphasizing "data dependency" Wednesday and saying if data does not hold up in 2019 the Fed may change course.

Stocks sank Wednesday and Thursday after the Fed's hike, pushing the Dow Jones Industrial Average and further into correction territory. However, U.S stocks opened Friday's session slightly higher.

Earlier this month, Williams, a voting member and vice chairman of the policymaking Federal Open Market Committee, said he expects the Fed to continue raising rates "over the next year or so," even while it pays close attention to possible risks highlighted by financial markets.

Wednesday on CNBC, Williams said he expects solid U.S. growth of around 3 percent this year and somewhat slower next year. Central bankers also are continuing "to monitor global economic and financial markets developments and their potential economic impact."

— CNBC's Kate Rooney contributed to this report.