The dollar eased slightly against the yen after rallying on Monday in response to Japan's announcement of another massive trade deficit.
Tokyo gave up early gains as the yen reversed course against the dollar, with the Nikkei ending 0.85% lower, giving up 123.61 points to finish at 14,388.77. Hong Kong ended down 0.13%, or 29.56 points, at 22,730.68.
Shanghai closed up 0.34%, or 7.00 points, at 2,072.83, Sydney gained 0.46%, or 25.1 points, to 5,479.3, and Seoul added 0.25%, or 5.00 points, to 2,004.22.
Business remained thin as traders returned from the long weekend. Markets in Sydney and Wellington will also be closed Friday for Anzac Day.
US shares jumped for a fifth straight session ON Monday thanks to solid earnings reports from firms including Halliburton and Hasbro. Attention is now on earnings reports expected this week from top firms including McDonald's, United Technologies and AT&T.
The Dow gained 0.25%, the S&P 500 rose 0.38% and the Nasdaq added 0.64%.
Wall Street's advances follow a torrid week earlier this month when tech players such as Twitter and Facebook were sold off on fears they were overvalued. Those companies have now clawed back much of their losses.
In Japan, the earnings season gets under way next week with the release of reports from big names including Honda, Panasonic and Japan Airlines.
On currency markets the dollar was at 102.50 yen compared to 102.62 yen late in New York.
The Japanese unit dipped Monday after the government said its trade deficit in March quadrupled year-on-year to $14 billion owing to the rising cost of importing fossil fuels and consumers rushing to buy before the April 1 sales tax hike.
The euro bought 141.47 yen and $1.3800 against 141.58 yen and $1.3794.
Oil prices were lower. New York's main contract, West Texas Intermediate for May delivery, was down $1.06 at $103.31 a barrel in afternoon trade. Brent North Sea crude for June declined 24 cents to $109.71.
Gold fetched $1,291.73 an ounce at 1045 GMT, compared with $1,287.37 on Monday.
In other markets, Jakarta ended up 0.12%, or 5.92 points, at 4,898.21. State miner Aneka Tambang rose 1.76% to 1,155 rupiah, while Indocement Tunggal Prakarsa slipped 0.98% to 22,775 rupiah.
Kuala Lumpur inched up 0.19%, or 3.490 points, to 1,866.42. Public Bank gained 0.9% to 20.38 ringgit, while YTL Corporation rose 1.5% to 0.65.
Manila closed 0.26% higher, adding 17.44 points to 6,784.95. SM Investments rose 1.15% to 746.50 pesos, BDO Unibank added 0.28 percent to 89.00 pesos and Megaworld advanced 2.24 percent to 4.57 pesos.
Mumbai fell 0.03%, or 6.46 points, to 22,758.37. Automobile tyre-maker MRF fell 7.14% to 21,879.50 rupees while Apollo Tyres dipped 5.58% to 167.40 rupees.
Singapore rose 0.67%, or 21.70 points, to 3,277.53. United Overseas Bank climbed 1.91% to S$22.45 while Singapore Airlines was up 0.58% at S$10.34.
Taipei rose 0.26%, or 23.52 points, to 8,974.71. Smartphone maker HTC added 1.58% to T$160.5 while PC firm Acer was 0.26% higher at T$19.4.
Wellington ended flat, edging up 1.59 points to 5,104.94. Air New Zealand added 0.48% to NZ$2.08 and Fletcher Building was off 0.21% at NZ$9.60.