The Dow Jones Industrial Average on Friday closed 746.94 points, or 3.29 per cent, dramatically higher to 23,433.16.
"We've been willing to revisit our views, very much willing to revisit our views, of what the natural rate is, and also our understanding of what it is", Powell said.
On Friday, the Labor Department reported the U.S. added 312,000 jobs in December, much above analyst expectations.
Trump's attacks had become so intense that they had raised concerns that he might be considering firing Powell, a development which could send the market into a further tailspin. The market bounce came after a volatile December selloff in which traders grew increasingly skeptical of the Fed's upbeat forecasts and plans to keep hiking interest rates in 2019.
Dallas Fed President Robert Kaplan said on Thursday that planned rate hikes should be halted for now, while on Friday Mester said she sees only one or two rate hikes this year.
Powell said that they are watching financial markets and their concerns.
"A solid set of job numbers and some comfortable words from the chairman of the Federal Reserve have been just the ticket to get markets into bullish mode", said Chris Beauchamp, chief market analyst at online trading platform IG.
Powell called the December jobs report "very strong" and said USA data seems "to be on track to sustain good momentum into the new year".
Saudi women to be informed of divorce via text message
The guardianship system has lead to Saudi Arabia considered as one of the most gender-unequal countries in the Middle East. According to lawyer Nisreen al-Ghamdi, some men now register divorce deeds at the courts without telling their wives.
Powell gave as an example the fact that in 2016, when Janet Yellen was Fed chair, the central bank began the year with a projection that it would raise rates four times that year but ended up raising rates only once because the economy hit a soft-patch.
Although still low by historical standards, this latest hike put interest rates at the highest level in almost a decade.
Mr Powell said he thought the recent market declines reflected concerns about slowing global growth and trade tensions - but are "well ahead of the data".
Still, with unemployment at 3.7 percent, some economists caution that inflation could move higher if labor shortages begin to bite - that's partly why the Fed hiked rate four times a year ago.
While it's not a real-economy measure, the Fed closely watches market volatility because it can feed through to consumer and business sentiment and the real economy. But it has been gradually reversing that stance over the past year, although the balance sheet still remains above $4 trillion.
Powell on Friday stressed that the Fed was prepared to adjust the pace at which it trimmed the balance sheet if necessary to support economic growth.
"Nothing's been scheduled, I would say that meetings between presidents and Fed chairs do happen", he told moderator and New York Times reporter Neil Irwin.
Trump has been vocal about his dissatisfaction with Powell, noting on Christmas Eve on Twitter, "The only problem our economy has is the Fed..."