Global markets, already upended by Trump's trade war, were hit at the start of the week by fears he was looking to remove central bank boss Jerome Powell for not cutting interest rates, with the US president calling him a "major loser" and "Mr. Too Late".
Experts warned such a move would deal a blow to the Fed's independence and spark a crisis of confidence in the world's top economy.
However, Trump tempered those fears on Tuesday. "I have no intention of firing him," he said.
Further comments by Trump on Tuesday indicating a more conciliatory approach to the trade war with China added to the positive market sentiment.
"These comments have given markets a sense of optimism that recent chaos might have peaked and we're heading towards calmer waters," said AJ Bell investment director, Russ Mould.
Wall Street's main equity indices, which had already gained more than two percent on Tuesday, rose again Wednesday.
The broad-based S&P 500 finished 1.7 percent higher.
Markets are climbing on "any headline that's less negative on trade," said Art Hogan of B. Riley Wealth Management.
"We've moved into a slightly more positive position but we still don't know what the endgame will be on trade," Hogan said
European stock markets also rallied, with Frankfurt gaining more than three percent.
Meanwhile, data showed that business activity in the eurozone remained "broadly unchanged" in April as manufacturing held up in the face of US tariffs despite waning confidence for the year ahead.
In Britain, however, the purchasing managers' index tumbled more than expected to a two-and-a-half-year low.
On trade, Washington has imposed additional tariffs of 145 percent on a range of products from China, while Beijing has replied with 125 percent duties on imports from the United States.
Trump acknowledged that the US levies were at a "very high" level and that it would "come down substantially".
On Wednesday, Treasury Secretary Scott Bessent told reporters Washington is "not yet" speaking with Beijing on tariffs, calling today's prohibitively high levies from both countries not "sustainable."
Gold, which had hit a record high above $3,500 Tuesday on a rush to safety, retreated to around $3,300 an ounce, while the dollar clawed back some of its recent losses against the pound, euro and yen.
"Looking at the dollar's more muted reaction, you get the feeling that it is more of a reluctant view that Trump is slowly backing down on trade tariffs. It is actions that count," said City Index and FOREX.com analyst Fawad Razaqzada.
In Asia, Hong Kong stocks surged on the back of a rally in tech firms including Alibaba and Tencent, and Tokyo's stock market also gained.
Taipei jumped more than four percent, helped by a seven percent surge in chip titan TSMC.
- Key figures at 2030 GMT -
New York - Dow: UP 1.1 percent at 39,606.57 (close)
New York - S&P 500: UP 1.7 percent at 5,375.86 (close)
New York - Nasdaq Composite: UP 2.5 percent at 16,708.05 (close)
London - FTSE 100: UP 0.9 percent at 8,403.18 (close)
Paris - CAC 40: UP 2.1 percent at 7,482.36 (close)
Frankfurt - DAX: UP 3.1 percent at 21,961.97 (close)
Tokyo - Nikkei 225: UP 1.9 percent at 34,868.63 (close)
Hong Kong - Hang Seng Index: UP 2.4 percent at 22,072.62 (close)
Shanghai - Composite: DOWN 0.1 percent at 3,296.36 (close)
Euro/dollar: DOWN at $1.1317 from $1.1421 on Tuesday
Pound/dollar: DOWN $1.3257 at $1.3332
Dollar/yen: UP at 143.49 yen from 141.57 yen
Euro/pound: DOWN at 85.34 pence from 85.67 pence
Brent North Sea Crude: DOWN 2.0 percent at $66.12 per barrel
West Texas Intermediate: DOWN 2.2 percent at $62.27 per barrel
burs-jmb/md
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