Sentiment was also mixed after the US president's signature budget bill scraped through the Senate, with optimism over the extension of deep tax cuts offset by warnings it could add around $3 trillion to the national debt.
A week before Trump's 90-day pause on "reciprocal" tariffs ends, few governments have struck deals to avert the taxes, though White House officials say several are in the pipeline.
And while the administration had set July 9 as the deadline to finalise pacts, investors largely expect that to be pushed back or countries given extra time.
However, the president said Tuesday he was "not thinking about the pause" and again warned he would end negotiations or hike some duties.
Among those in his sights was Japan, which he slammed this week over US rice and auto exports to the country.
"I'm not sure we're going to make a deal. I doubt it with Japan, they're very tough. You have to understand, they're very spoiled," he said Tuesday.
He added that Tokyo had "ripped us off for 30, 40, years".
It could pay a tariff of "30 percent, 35 percent, or whatever the number is that we determine, because we also have a very big trade deficit with Japan", he warned.
The remarks, which follow several visits by Japanese officials to Washington, jolted hopes that deals can be cut.
Tokyo stocks fell, extending Tuesday's losses of more than one percent.
"With domestic elections around the corner, Tokyo can't easily open the rice market," said Stephen Innes at SPI Asset Management. "But without concessions on autos, the lifeblood of its export economy, Japan stands exposed."
He added: "The auto sector, nearly a tenth of Japan's (gross domestic product), is directly in the crosshairs. It's not just about tariffs -- it's about visibility.
"Japan is being made an example of, and markets are watching who's next."
Asia Society Policy Institute vice president Wendy Cutler told AFP that "Japan's refusal to open its rice market, coupled with the US resistance to lowering automotive tariffs, may lead to the reimposition of Japan's 24 percent reciprocal tariff".
Elsewhere in Asia, Seoul, Shanghai, Manila, Mumbai, Bangkok and Jakarta fell while Hong Kong, Sydney, Singapore, Taipei and Wellington edged up.
London, Paris and Frankfurt were all up in the afternoon.
In Washington senators passed Trump's "Big, Beautiful Bill" he says will boost the economy by extending tax cuts and slashing spending on programmes such as Medicare.
The legislation now faces a tough passage through the House of Representatives, where some Republicans have raised concerns about its cost amid already heightened fears over the country's finances.
The dollar remained under pressure as bets on a Federal Reserve interest rate cut intensify ahead of US jobs data this week.
While most traders see a reduction in September, speculation is growing that a weak non-farm payrolls reading could boost the chances of a move this month.
The Dollar Index, which compares the greenback to a basket of major currencies, fell 10.8 percent in the first half of the year, its steepest decline since it became the global benchmark currency.
In company news Australian flag-carrier Qantas sank more than two percent in Sydney after saying it was probing a "significant" cyberattack where hackers infiltrated a system containing sensitive data on six million customers.
And Hong Kong-listed Chinese tech titan Alibaba dipped after saying it will issue US$7 billion in subsidies for certain purchases.
- Key figures at around 0810 GMT -
Tokyo - Nikkei 225: DOWN 0.6 percent at 39,762.48 (close)
Hong Kong - Hang Seng Index: UP 0.6 percent at 24,221.41 (close)
Shanghai - Composite: DOWN 0.1 percent at 3,454.79 (close)
London - FTSE 100: UP 0.1 percent at 8,979.91
Euro/dollar: DOWN at $1.1774 from $1.1806 on Tuesday
Pound/dollar: DOWN at $1.3707 from $1.3740
Dollar/yen: UP at 143.92 yen from 143.41 yen
Euro/pound: UP at 85.90 pence from 85.87 pence
West Texas Intermediate: UP 0.1 percent at $65.53 per barrel
Brent North Sea Crude: UP 0.2 percent at $67.25 per barrel
New York - Dow: UP 0.9 percent at 44,494.94 (close)
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