Trump, in an appearance Wednesday at the United Nations, said a deal with China was getting closer, sending equities higher despite concerns over the launch of an impeachment inquiry against the mercurial leader.
The remarks came just a day after Trump railed against Chinese "abuses" at the UN summit, comments that had been seen as among the factors causing stocks to fall Tuesday.
Connor Campbell, analyst at Spreadex trading group, said "investors chose to buy into Trump's trade optimism, allowing the markets to push higher".
Trump on Wednesday also said Washington and Tokyo had taken a major step towards sealing a comprehensive new trade deal, which will see Japan cut tariffs on $7 billion of US farm exports while the US would cut tariffs on some Japanese agricultural goods.
"Investors have been 'trade war' bearish for so long that any sliver of optimism is cheered," Stephen Innes, Asia Pacific market strategist at AxiTrader, said in a note.
The Japanese deal also "suggests the president is open to an 'interim' trade deal, possibly signalling he is willing to negotiate one with China", Innes said.
Asian markets largely cheered Trump's positive comments on trade.
Elsewhere, crude prices slipped after an unexpected rise in US inventory and a swift recovery in Saudi Arabia's output following the September 14 attacks on its oil infrastructure.
The pound was little changed. The British currency had pulled back after it rallied on Tuesday on the belief that the odds of a no-deal Brexit had fallen..
"It will probably take a Brexit agreement signed and sealed to give it new upside momentum," said Jeffrey Halley, senior market analyst at OANDA.
On the corporate front, shares in Airbus were unchanged at 121 euros in Paris after sources revealed that the European aerospace giant has been hit by a series of attacks by hackers targeting its suppliers in search of commercial secrets, adding they suspected a Chinese link.
AFP spoke to seven security and industry sources, all of whom confirmed a spate of attacks in the past 12 months but asked for anonymity because of the sensitive nature of the information they were sharing.
- Key figures around 1115 GMT -
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London - FTSE 100: UP 1.0 percent at 7,361.44 points
Frankfurt - DAX 30: UP 0.4 percent at 12,283.83
Paris - CAC 40: UP 0.7 percent at 5,620.22
EURO STOXX 50: UP 0.5 percent at 3,530.40
Hong Kong - Hang Seng: UP 0.4 percent at 26,041.93 (close)
Shanghai - Composite: DOWN 0.7 percent at 2,929.087 (close)
Tokyo - Nikkei 225: UP 0.1 percent at 22,048.24 (close)
New York - Dow: UP 0.6 percent at 26,970.71 (close)
Euro/dollar: DOWN at $1.0932 from $1.0944 at 2100 GMT
Pound/dollar: DOWN at $1.2349 from $1.2355
Euro/pound: DOWN at 88.53 from 88.56 pence
Dollar/yen: DOWN at 107.59 yen from 107.77
Brent North Sea crude: DOWN 0.2 percent at $62.25 per barrel
West Texas Intermediate: DOWN 0.1 percent at $56.46 per barrel