But dealers also remained hesitant before the release this week of Chinese third-quarter growth figures, as evidence accumulates of a slowdown in the world’s second-biggest economy.
In Japan, telecoms giant Softbank surged by more than 10 percent, clawing back some of its huge losses in the previous two sessions, after formally announcing it will buy US wireless provider Nextel Sprint for $20 billion.
Tokyo rose 1.44 percent, or 123.38 points, to 8,701.31, Sydney gained 0.18 percent, or 8.1 points, to 4,491.5 and Seoul climbed 0.83 percent, or 15.95 points, to 1,941.54.
In the afternoon Hong Kong was up 0.23 percent and Shanghai was up 0.37 percent.
Trading started positively with the news out of Washington that retail sales, the main driver of the US economy, had unexpectedly risen 1.1 percent in September.
The Commerce Department also revised up retail sales for July and August, and said that even excluding volatile data on vehicles and petrol, sales were still up 0.9 percent last month.
Helping the mood on Wall Street, banking giant Citigroup reported an 88 percent drop in third-quarter profit, not as bad as had been forecast.
The Dow gained 0.72 percent, its biggest jump in more than a month, while the S&P 500 rose 0.81 percent and the Nasdaq added 0.66 percent.
On currency markets the euro was trading higher thanks to an improved appetite for risk. In afternoon Asian trade it was buying $1.2965, up from $1.2950 late Monday in New York, while it rose to 102.30 yen from 101.89 yen.
The dollar stood at 78.87 yen, up slightly from 78.66 in New York.
The main focus of interest this week is on China, which will release Thursday its growth figures for July-September, with many hoping for an improvement on recent data that has shown a marked slowdown.
Hopes were given a boost at the weekend by trade figures that showed China’s exports surged almost 10 percent last month.
Also Thursday the European Union holds a summit, with a possible bailout for Spain on the agenda along with Greece’s push to renegotiate its own rescue deal.
Reports indicate that Athens could be given more time to repay its huge debts, following comments from International Monetary Fund chief Christine Lagarde in Tokyo that an extra two years would be acceptable.
Softbank surged 10.76 percent after the Japanese company confirmed it would take 70 percent of Sprint Nextel, the number-three US cellphone carrier, in the biggest-ever overseas acquisition by a Japanese firm.
The bounce followed a dive of more than 20 percent over the previous two days after the firm said it was in talks over a buyout.
“It’s official now,” a senior strategist at a Japanese brokerage told Dow Jones Newswires. “Some buyback is likely.”
Oil prices fell. New York’s main contract, light sweet crude for November delivery, shed five cents to $91.80 a barrel. Brent North Sea crude for November delivery fell $1.52 to $114.28.
Gold was at $1,737.87 at 0600 GMT compared with $1,745.05 late Monday.