New York Fed President John Williams took a step Friday toward undoing the blunt blow to markets delivered by the Federal Reserve and Fed Chairman Jerome Powell on Wednesday.

Stocks initially jumped, the dollar rose and bonds sold off, after Williams indicated the Fed would be flexible and could consider changing policy if the economy or financial conditions warrant. But the stock market erased those gains, which had pushed the Dow up over more than 300 points.

In an interview on CNBC's "Squawk on the Street," Williams made it clear the Fed would be dependent on economic data and other signs of business activity and sentiment before making a decision on interest rates. He also said the Fed will go into next year with its "eyes wide open" and reconsider programs such as its balance sheet reduction, if necessary.

"People are going to tell you the Federal Reserve softened its position, but I really think the market is coming around to the Fed's views," said Marc Chandler, chief market strategist at Bannockburn Global Forex. "The median [interest rate forecast] is not the Fed's view. Williams was playing up that these things are not carved in stone."

The Fed unnerved markets Wednesday when it hiked interest rates and released a statement that was slightly more hawkish than expected. In its forecast, it reduced its median interest rate forecast, derived from all Fed officials' opinions, to two rate hikes from three. But some market pros had been hoping the Fed might consider reducing its expectations even further, in line with its forecast that growth would slow next year and it is monitoring global economic weakness.

"It's kind of just a reassessment trade. People took a step back and looked at what happened Wednesday and came to the conclusion it really isn't all that different from what we should have expected," said Ward McCarthy, chief financial economist at Jefferies.

Powell said the Fed was happy to maintain its balance sheet reduction on "autopilot." That comment and other concerns about the Fed helped drive stocks lower, with the Dow losing more than 800 points Wednesday and Thursday. The Dow was up about 134 points to the psychological 23,000 level in late morning trading.

"I think even though Powell said autopilot, I think it was understood to address economic weakness, the Fed will use other policy tools. Everybody said the Federal Reserve may have made a policy mistake, but I would think today the market is correcting its overexaggerated response. Williams is not breaking any new ground. He saying it differently, but he's reading from the same chorus book," said Chandler.

Powell's comment on the balance sheet rattled markets, as stocks have lost 15 percent or more from their highs and credit spreads have widened in recent weeks. Those factors have led to more market chatter about whether the Fed balance sheet program is unnecessarily removing liquidity from markets.

"We did not make a decision to change the balance sheet normalization right now, but as I said, we're going to go into the new year with eyes wide open, willing to read the data, and reassess the economic outlook and take the right policy decisions," Williams told CNBC.

The Fed is allowing about $50 billion a month to roll off its balance sheet as mortgage securities and Treasurys mature. Previously, it was making repurchases to replace all securities that matured.

"As far as the balance sheet goes, that is the great unknown. They've never given us a definitive objective of what they want the size to be," said McCarthy. "They created an impression that they wanted it down to $3 trillion. It's now about $4 trillion. If they maintain the caps throughout 2019, it will be down to around $3 trillion."

McCarthy said he expects the balance sheet to become more a part of the policy discussion next year. Quantitative easing, or the Fed's purchases of securities after the financial crisis, ballooned the balance sheet.

"What became apparent was [QE] was squeezing volatility and creating a one-way trade," he said. "Shrinking the size of the balance sheet, I think, would increase volatility and make trades that are two-way. So far, that's what we're seeing."

Treasury yields initially moved higher after Williams' remarks but were steady in late morning trading.

"I did think Williams tried to walk back some of what Powell said," said Peter Boockvar, chief investment strategist at Bleakley Advisory Group. But Boockvar said for now the Fed continues to reduce the balance sheet. "I don't think that provided any relief on the rate side."

McCarthy said the Fed sometimes becomes the "national scapegoat."

"That's what's happening here," said McCarthy. "It would be truly disturbing if the Fed changed what they thought was proper monetary policy because the market wanted them to do something different. Right now, we're in the midst of a maelstrom. Nobody said it would be easy. For years, the Fed was criticized for putting the market on drugs. Now the Fed is trying to take the market off those drugs and people are complaining."