By Agence France-Presse
Japan's benchmark Nikkei-225 powered higher, gaining 1.25 percent on what traders called a "technical rebound" after a sharp fall on Monday.
However, shares in China, South Korea and Hong Kong were lower as cautious traders appeared unwilling to make big bets after last week's bruising declines.
The Chinese benchmark Shanghai Composite, which has suffered more than most markets in the recent rout, lost almost one percent in late Asian trade.
Global markets have been rocked in recent days by fears over spiking oil prices, rising US long-term interest rates and an attack by US President Donald Trump on his own central bank and its policies.
Investors have now entered a "stalemate period to rethink the plethora of looming market uncertainties, ambiguities and flat out worries", said Stephen Innes from OANDA trading.
"But this relative calm belies the building storm clouds on the horizon."
After a see-saw session on Wall Street, the Dow Jones closed down 0.4 percent and the broader S&P 500 was down just more -- at 0.6 percent.
In commodities trading, the oil price continued to climb amid ongoing geopolitical tensions surrounding Saudi Arabia, with accusations that journalist Jamal Khashoggi was murdered in the Kingdom's consulate in Istanbul.
Trump said overnight he would send Secretary of State Mike Pompeo to find out "first-hand what happened, what they know, what's going on".
Margaret Yang Yan, market analyst at CMC Markets Singapore said: "Against the backdrop of the softening dollar and rising political tensions between the US and Saudi due to the disappearance of (Khashoggi), crude oil prices stopped bleeding and started to rebound."
Turning to foreign exchange markets, the pound suffered further falls in early Asian trade as the possibility of a "no deal" Brexit looms, before recovering slightly.
EU President Donald Tusk said he remained "hopeful and determined" that Britain and the bloc could clinch an amicable divorce deal.
However, he added: "We must prepare the EU for a no-deal scenario, which is more likely than ever before."
Key figures around 0630 GMT
Tokyo - Nikkei 225: UP 1.3 percent at 22,549.24 (close)
Hong Kong - Hang Seng: DOWN 0.2 percent at 25,399.41
Shanghai - Composite: DOWN 0.8 percent at 2,548.48
Euro/dollar: UP at $1.1569 from $1.1550 at 0230 GMT
Pound/dollar: UP at $1.3147 from $1.3110 at 0230 GMT
Dollar/yen: DOWN at 112.06 from 112.08 yen at 0230 GMT
Oil - West Texas Intermediate: UP 2 cents at $71.86 per barrel
Oil - Brent Crude: UP 11 cents at $81.02 per barrel
New York - Dow Jones: DOWN 0.4 percent at 25,250.55 (close)
London - FTSE 100: UP 0.5 percent at 7,029.22 (close).