Greater China markets pulled back slightly. Hong Kong's Hang Seng Index declined 0.65 percent, with the energy and financials sectors weighing. Mainland stock indexes saw smaller losses: The Shanghai composite edged down by 0.48 percent and the Shenzhen composite shed 0.23 percent.
Over in Sydney, the S&P/ASX 200 gave up early gains to slip 0.15 percent as energy names dragged on the broader index. The materials and heavily weighted financials subindexes inched higher after coming under pressure in the last session.
MSCI's index of shares in Asia Pacific excluding Japan slipped 0.11 percent in Asia morning 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.
European markets got a boost on Tuesday from that announcement: The pan-European Stoxx 600 rose 0.27 percent and Germany's DAX advanced 0.71 percent as autos notched gains.
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 paused after hitting a five-month high against a basket of currencies earlier in the week. That dollar index was steady at 93.549 at 9:37 a.m. HK/SIN.