Later in the day, the U.S. Federal Reserve is widely expected to cut interest rates for the first time since the financial crisis more than a decade ago. The expected easing has supported risk asset prices worldwide.
MSCI's broadest index of Asia-Pacific shares outside Japan pared losses to trade down 0.5% but earlier fell to the lowest since June 19, while Japan's Nikkei declined by 0.7%.
In early European trade, the pan-region Euro Stoxx 50 futures rose 0.1%, German DAX futures were up 0.1% and Britain's FTSE futures were little changed.
Major Wall Street stock averages ended slightly lower on Tuesday, with the S&P 500 losing 0.26%, after Trump warned China against waiting out his current presidential term before finalising a trade deal.
As a new round of U.S.-China trade negotiations started in Shanghai, Trump tweeted that, if he wins re-election in November 2020, the outcome could be no agreement or a harsher one.
"We expect the Fed to cut rates by 25 basis points and keep the door open to further rate cuts, which should be sufficient to keep markets satisfied," said Mayank Mishra, a macro strategist at Standard Chartered Bank in Singapore.
"U.S.-China trade talks have just started after a long hiatus. I don't think expectations are that high."
After the closing bell in the United States, Apple shares rose 4.2% as its April-June earnings beat estimates and CEO Tim Cook cited "marked improvement in Greater China".
In Asia, S&P 500 mini futures rose 0.3%.
The S&P 500 index has risen 2.4% so far this month, bolstered by expectations for Fed easing.
Fed funds rate futures are now fully pricing in a 25 basis point rate cut on Wednesday and another 25 basis point reduction by September.
U.S. consumer spending and prices rose moderately in June, pointing to slower economic growth and benign inflation that cemented expectations of Fed rate cuts.
Trump on Tuesday reiterated his call for the Fed to make a large interest rate cut, saying he was disappointed in the U.S. central bank and that it had put him at a disadvantage by not acting sooner.
In addition to worries about trade talks with the United States, Chinese shares suffered a further setback on Wednesday after the ruling Communist Party's top decision-making body said late on Tuesday it will not use the property market as a form of short-term stimulus.
The blue-chip CSI300 index fell 0.7%, with a slide in shares of property developers leading a retreat in the broader market.
China will also step up efforts to boost demand, the Politburo said, which takes on more urgency after the country's official PMI on Wednesday showed factory activity shrank for a third straight month due to the trade war.
South Korean stocks fell to the lowest since early January on trade war jitters but then trimmed losses to trade down 0.2%. Weak quarterly results from Samsung Electronics added to concerns about an oversupply of memory chips.
Samsung, closely watched as a barometer of electronics demand, warned that Japanese curbs on the export of chip-making materials are weighing on its outlook and likely to hurt third-quarter results.
In currency markets, the British pound remains near a 28-month low hit the previous day on growing concerns about a disorderly Brexit.
Sterling traded at $1.2148, not far from $1.2120 marked on Tuesday. It has fallen 4.2% so far this month, on course to log its worst monthly performance since October 2016.
"Trump's comments suggest that U.S.-China trade negotiations are not going well, which is a new negative factor for the markets," said Osamu Takashima, head of G10 FX strategy at Citigroup Global Markets Japan in Tokyo.
"In addition to Brexit, markets are starting to price in the Bank of England moving to dovish from hawkish at its next meeting, so this drives sterling depreciation," Citigroup's Takashima said.
Other major currencies were less volatile with the yen flat at 108.53 yen to the dollar. The euro stood little changed at $1.1157.
U.S. West Texas Intermediate (WTI) crude gained 0.69% to $58.45 per barrel after earlier reaching a two-week high of $58.53 in Asia.