By Agence France-Presse
Trump and Jean-Claude Juncker announced the agreement after talks Wednesday at the White House, as the two major economies sought to end the dispute that had rattled markets and sparked fears of an all-out global trade war.
The plan means Washington will not follow through with a threat to impose tariffs on autos, which would hurt the dominant German car industry, while the pair also vowed to look at existing duties on steel and aluminium imposed by the US, that had angered the EU.
The news sent US stocks surging in the final hours of trading Wednesday, with the Nasdaq hitting a record high, and Asian bourses initially made gains at the open Thursday.
But most major exchanges quickly fell into negative territory, with analysts blaming the lacklustre US results, which included social networking giant Facebook and major carmakers.
The EU-US deal had given American equities a "late boost", said Jingyi Pan, market strategist at trading group IG.
But she added that "the blips in the latest US earnings performances look to undercut some of these positive inspirations for the Asian region".
Tokyo was down about 0.1 percent in late morning trade, with speculation that the Bank of Japan could review its buying of exchange-traded funds to invest in listed companies at a meeting next week adding to negative sentiment.
Shanghai was off almost 0.2 percent, Hong Kong was down 0.3 percent and Sydney was flat.
South Korea bucked the negative trend, rising 0.6 percent, as investors cheered official data showing that economic growth in the second quarter met expectations.
The biggest shock of Wednesday's results came from Facebook, which reported a stunningly weak financial outlook that raised fresh concerns for the company giant as it tries to recover from the impact of data protection scandals and investigations.
After-hours trade saw Facebook shares plunge by some 21 percent, wiping out an estimated $130 billion in market value if the slump is confirmed at Thursday's market opening.
Ford reported a sharp drop in second-quarter earnings while General Motors reported a jump in second-quarter profit, but cut its full-year profit forecast. Fiat Chrysler also reported disappointing results.
In currency markets, the euro firmed after the the EU-US trade announcement, while the dollar was down. The euro was "benefiting from a reprieve in the US trade war", said Stephen Innes, head of Asia-Pacific trading at Oanda.
Traders were also awaiting a meeting the European Central Bank later Thursday, although analysts expect the bank to leave unchanged its plans to end massive stimulus for the eurozone by December.
Key figures at 0320 GMT
Tokyo - Nikkei 225: DOWN 0.1 percent at 22,592.23
Hong Kong - Hang Seng: DOWN 0.5 percent at 28,771.69
Shanghai - Composite: DOWN 0.3 percent at 2,893.19
Euro/dollar: UP at $1.1737 from $1.1729
Pound/dollar: UP at $1.3204 from $1.3193
Dollar/yen: DOWN at 110.780 yen from 110.98 yen
Oil - Brent Crude: UP 48 cents at $74.41 a barrel
Oil - West Texas Intermediate: UP 10 cents at $69.40 a barrel
New York - Dow: UP 0.7 percent at 25,414.10 (close)
London - FTSE 100: DOWN 0.7 percent at 7,658.26 (close)