The mainland Chinese markets, closely watched in relation to Beijing's ongoing dispute with Washington, slipped by the end of their trading day. The Shanghai composite declined 0.61 percent to close at about 2,649.81 and the Shenzhen composite fell 0.484 percent to finish at around 1,380.78.
The Caixin Services Purchasing Managers' Index, which measures economic activity in China's services sector, rose to 53.8 in November — its highest in five months — as compared to 50.8 in October.
Earlier in the day, China's Ministry of Commerce said in a statement on its website that the weekend meeting between Trump and Chinese President Xi Jinping was successful. The ministry also said the two countries will push ahead with negotiations within 90 days, and Beijing will work to address issues agreed upon as quickly as possible.
Meanwhile, the Hang Seng index in Hong Kong also fell by around 1.6 percent as of its final hour of trading. Shares of vehicle maker Baic Motor dropped 10.30 percent following a Bloomberg report that Germany's Daimler is considering increasing its stake in its joint venture with the Chinese firm.
Rest of Asia mostly see losses
In Australia, the ASX 200 fell 0.78 percent to close at 5,668.40, with most sectors seeing losses on the day. The moves came after the country's gross domestic product (GDP) data for the third quarter came in below expectations.
Real GDP expanded 0.3 percent on-quarter in the three months through September and 2.8 percent on-year, according to data released by the Australian Bureau of Statistics on Wednesday.
Economists polled by Reuters had expected 0.6 percent growth on quarter and a 3.3 percent on-year increase.
Following the release of the data, the Australian dollar fell 0.57 percent to trade at $0.7295. It had earlier seen a high of $0.7355.
Wall Street takes a dive
The yield on the three-year Treasury note surpassed its five-year counterpart on Monday. When a so-called yield curve inversion happens — short-term yields trading above longer-term rates — a recession could follow, though it is often years away after the signal triggers.
Stocks began falling to their lows of the day after Jeffrey Gundlach, CEO of Doubleline Capital, told Reuters this inversion signals that the economy "is poised to weaken."
The CBOE Volatility Index, popularly known as the VIX, leaped about 26.16 percent to 20.74. The VIX measures implied volatility on S&P 500 index options. It had earlier hit a high of 21.94 — its highest levels since Nov. 23 when it touched a high of 22.65.
Confusion over US-China trade agreement
The two economic powerhouses have been locked in an ongoing trade war, which has continued to rock global markets for much of 2018.
The U.S. and China agreed over the weekend to hold off on any additional tariffs on each other's goods on Jan. 1, so that trade talks can continue. But discrepancies over when that truce would begin has led to confusion, with conflicting messages coming from within the White House as well as differing opinions from Trump, Washington and Beijing over the actual details of the agreement.
"After the meeting, it was clear that there is no comprehensive deal but just a truce and that both sides are putting out somewhat different statements," Dariusz Kowalczyk, senior emerging market strategist at Credit Agricole CIB, told CNBC's "Street Signs" on Wednesday.
"The markets shouldn't be surprised by the fact that there is some discrepancy between what both sides are perceiving as to what was agreed," he said.
The Japanese yen, widely viewed as a safe-haven currency, traded at 112.99 against the dollar after strengthening from above 113.5 yesterday.
— Reuters and CNBC's Fred Imbert, Christina Wilkie and Yen Nee Lee contributed to this report.