MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.1 percent in early trade.
Japan's Nikkei slipped 0.3 percent.
South Korea's KOSPI gained 0.3 percent, with the biggest stock Samsung Electronics flat after Monday's 1.6 percent slump. Naver Corp. and LG Innotek, which led Asian losses on Monday, also recovered.
On Wall Street, tech giants including Apple, Alphabet, Facebook and Microsoft continued to be sold off for the second consecutive day.
That dragged the Nasdaq down 0.5 percent, the S&P 500 0.1 percent and the Dow Jones Industrial Average 0.2 percent.
"I don't sit in the camp that we will see a prolonged pullback in U.S. tech, but there is a good chance this hot sector now underperforms and I had been suggesting increasing exposure to U.S. financials as a trade," Chris Weston, chief market strategist at IG in Melbourne, wrote in a note.
In currencies, the Canadian dollar held on to Monday's strong gains, after a Bank of Canada official said the central bank would assess if it needs to keep interest rates at near-record lows as the economy grows. That was a change in tone for the central bank, which said earlier this year that rate cuts remain on the table.
The so-called loonie strengthened about 0.1 percent to trade at C$1.33 to the dollar, extending Monday's 1.1 percent gain.
"It feels like a long time since markets have been treated to unscheduled hints of tightening, and this was quite apparent when you saw the positive reaction of CAD crosses overnight," Matt Simpson, senior market analyst at ThinkMarkets in Melbourne, wrote in a note.
The dollar failed to make up losses against the yen ahead of a widely expected interest rate increase by the U.S. Federal Reserve this week. It was flat at 109.95 yen, after falling 0.4 percent on Monday.
The dollar index, which tracks the greenback against a basket of trade-weighted peers, was marginally higher at 97.177.
The euro inched lower to $1.12.
In commodities, oil advanced on signs of inventory declines in the United States and news that Saudi Arabia would limit volumes of crude to some Asian buyers in July and deepen cuts to the U.S. market.
U.S. crude rose 0.3 percent to $46.19 a barrel.
Global benchmark Brent added 0.2 percent to $48.41.
© Thomson Reuters 2017