The Dow climbed 617 points, or 2.5 percent, to 25,366, its biggest gain in eight months.
Referring to the Fed's gradual increases in its benchmark rate, Powell said, "there is no preset policy path". In October, he said rates were still well below neutral.
Market reaction reflected investors' fears that the Fed might end up making the kind of mistake Mr. Powell talked about - tightening policy too much because of a false read on where neutral is, at a time when clouds had begun to form on the economic horizon.
The Japanese yen rose 0.1 percent. But the likely pace of rate increases next year remains a subject of speculation.
He also said the central bank does not see "dangerous excesses" in stock markets and the financial system now is "substantially more resilient" than it was before the 2008 financial crisis.
But the report highlighted stock prices that are high by some measures, commercial real estate values "growing faster than rents" and the willingness of lenders to fund risky corporate loans. "And Chair Powell will have another opportunity to sculpt the market's opinion a bit further if he's not happy with how they interpreted his recent remarks".
Since then, key officials including Vice Chairman Richard Clarida and New York Fed President John Williams have seemingly walked back the remark.
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His comments briefly pushed the USA 10-year bond yield below 3 percent, its lowest since mid-September.
Trump has repeatedly attacked Powell for continuing to raise the benchmark lending rate, which Trump says undermines the work he is doing to juice the USA economy.
Should any of a number of outside shocks occur, such as an escalating trade war between the U.S. and major trading partners, a messy breakup between Britain and the European Union, or a crisis in emerging markets, "the resulting drop in asset prices might be particularly large, given that valuations appear elevated relative to historical levels".
"Many participants indicated that it might be appropriate at some upcoming meetings to begin to transition to statement language that placed greater emphasis on the evaluation of incoming data in assessing the economic and policy outlook", the minutes said.
US law says Fed officials - and those of other independent agencies - can be "removed for cause", according to a report by The Washington Post on Wednesday.
But many economists warn that by attacking the Fed for raising rates, Trump is actually putting pressure on the central bank to raise rates to demonstrate its political independence. Powell became Fed chair in February this year after being nominated by Trump and confirmed by the Senate. Trump has complained that the Fed is threatening to undo the economic stimulus being provided by the tax cuts and that its rate hikes are unnecessary because inflation has remained relatively low.
With the Fed signaling fewer than three rate hikes next year, investors are being forced to adjust their U.S. Treasury bond and Japanese Treasury bond portfolios.