Greater China markets pulled back. Hong Kong's Hang Seng Index declined 1.42 percent by 3:29 p.m. HK/SIN, hurt by falls in financials and energy.
Mainland stock indexes saw similar losses: The Shanghai composite dropped 1.4 percent to close at 3,169.24, its largest single-day fall in around a month, according to Reuters. The smaller Shenzhen composite slid 1.1 percent to end at 1,834.72.
Coal miners came under pressure, with shares of China Shenhua down 6.16 percent in Hong Kong by 3:32 p.m. HK/SIN and lower by 6.95 percent in Shanghai. That came as Chinese authorities intervened in the coal market, Reuters reported.
Over in Sydney, the S&P/ASX 200 slipped 0.16 percent to close at 6,032.50 as energy names dragged on the broader index. Meanwhile, MSCI's index of shares in Asia Pacific excluding Japan edged down by 0.6 percent in Asia afternoon trade.
Declines came after President Donald Trump said he was "not satisfied" with bilateral trade talks with China that occurred last week, but called them a "start" to working out the U.S. trade imbalance with Beijing. U.S. stocks closed lower following those comments despite starting the session on positive footing.
Still on the issue of trade, China announced on Tuesday that it would reduce tariffs on some vehicles to 15 percent from as much as 25 percent. Tariffs on certain automotive parts would also be cut.
Global stock markets had been buoyed earlier in the week by fading jitters over U.S.-China trade tensions after the two sides met in Washington for talks. U.S. Treasury Secretary Steven Mnuchin's comment that negotiations had made "very meaningful progress" saw the Dow Jones industrial average close above the 25,000 level on Monday for the first time since March.
On the geopolitical front, Trump said Tuesday there was a "substantial chance" that a summit with North Korean leader Kim Jong Un "may not work out." Trump's comments came as he met South Korean President Moon Jae-in ahead of a planned meeting, scheduled for June 12, with Kim.
In currencies, the dollar edged up against a basket of currencies ahead of minutes from the Federal Reserve which are expected during U.S. hours. The dollar index was firmer at 93.788, but still below a five-month high reached earlier in the week.
In corporate news, shares of Australia's Santos plunged 8.39 percent after the oil and gas producer rejected a takeover offer from Harbour Energy. The offer did not represent the full value of the company, Santos said in a release, adding that it had also ended discussions with Harbour.