Nikkei 225 index added 1.3% to 40,125.60, the Kospi advanced 0.2% to 2,627.92 and the S&P/ASX 200 was 0.8% higher to 8,321.40
Asian shares gained on Tuesday after Wall Street rose to more records, though markets in China were mostly down.
U.S. futures rose while oil prices dropped more than $2 a barrel.
Tokyo’s Nikkei 225 index added 1.3% to 40,125.60, while the Kospi in Seoul advanced 0.2% to 2,627.92.
In Australia, the S&P/ASX 200 was 0.8% higher to 8,321.40.
Chinese shares extended losses after the government reported late Monday that growth in exports declined sharply in September, adding to signs of weakness in the economy.
The Shanghai Composite index slipped 0.5% to 3,267.13 while the Hang Seng in Hong Kong tumbled 1.3% to 20,810.11.
Market participants continue to seek for clarity around fiscal stimulus support from Chinese authorities, but the lack of commitment remains a source of reservation for risk-taking in Chinese equities, Yeap Jun Rong of IG said in a commentary.
Also early Tuesday, the dollar dropped to 149.70 Japanese yen from 149.83 yen. The euro slid to $1.0895 from $1.0911.
U.S. benchmark crude declined $2.25 to $71.58 per barrel. Brent crude, the international standard, stumbled $2.33 to $75.13 per barrel.
On Monday, Wall Street hit all-time highs.
The S&P 500 jumped 0.8% to build on its record set on Friday, closing at 5,859.85. It is coming off its fifth consecutive winning week and is on track for its longest weekly winning streak of the year.
The DJIA gained 0.5% to 43,065.22, adding 201 points to its own record. The Nasdaq composite added 0.9% to 18,502.69.
The gains followed relatively quiet trading in Europe, while the U.S. bond market remained closed for the day due to a holiday.
Prices also dropped for copper and other commodities. That helped drive down prices for miners, such as Freeport-McMoRan, which dropped 2.3% for one of the larger losses in the S&P 500.