Jerome Powell said that the central bank was "listening sensitively" to stock markets after the sell-off last month and would be "patient" with its interest rate policy.
On December 19, the Federal Reserve increased the interest rate for the fourth time in 2018 - from 2.25 percent to 2.5 percent.
"Despite this dovish tone, we are sceptical", Schenker said in a note.
There were concerns that the data would let the Fed stick with its projection for two interest rate hikes in 2019, but traders kept bets that the central bank will hold fire this year and begin cutting rates in 2020.
The Labour Department reported Friday that USA employers added a net 312,000 new positions in December, smashing economists' expectations.
He added: "We're listening with sensitivity to the message that markets are sending and we're going to be taking those downside risks into account as we make policy going forward". "But what I do know is that we will be prepared to adjust policy quickly and flexibly and to use all of our tools to support the economy should that be appropriate to keep the expansion on track".
Powell called the jobs report "very strong" and said he was also encouraged by the rise in the labour force participation rate and gains in wages, which he said "for me at this time does not raise concerns about too high inflation". A third Fed president, Thomas Barkin of Richmond, said he is hearing more concerns about economic risks and trade.
"If the President asked you to resign, would you do it?"
In response to questions, Powell also signaled a willingness to include changes to the Fed's gradual run-off of its balance-sheet in any review of monetary policy.
Speaking after months of volatility in world bond and stock markets, Powell avoided some of the communication missteps that in the past have roiled rather than calmed investors. "The Fed is going loco and there's no reason for them to do it".
The head of the Fed, once confirmed by the Senate, can only be removed "for cause", not a policy disagreement.
Mr Trump named Mr Powell to the helm of the Fed at the start of the year but has been a frequent and vocal critic, blaming Mr Powell and the Fed for raising rates which he says pose a threat to his economic agenda - an unprecedented public berating that breaks with recent norms.