The Nikkei 225 in Tokyo rose 1.2 per cent to 14,627.66 after the latest quarterly "tankan" survey showed a sharp improvement from the prior period. Large manufacturers were especially upbeat, with a reading of positive 12, up from 4 in the July survey.
Markets in mainland China and Hong Kong are closed for public holidays and couldn't react to a survey showing that manufacturing in the world's No. 2 economy barely expanded in September.
Tuesday's report by the China Federation of Logistics and Purchasing showed manufacturing expanded for the third month in a row. But the group's purchasing managers' index rose by only a fraction to 51.1 last month from 51.0 in August, less than economists expected.
The federation's report comes a day after a private survey by HSBC also indicated weaker than expected growth in China's massive manufacturing sector.
Elsewhere, South Korea's Kospi rose 0.4 per cent to 2,004.77. Australia's S&P/ASX 200 gained 0.1 per cent to 5,223.10. Benchmarks in Singapore, Taiwan and Indonesia also rose. New Zealand and Malaysia fell.
On Wall Street, stocks fell Monday amid worries that a budget fight in Washington could lead to a failure to raise the nation's borrowing limit. The so-called debt ceiling has to be raised or the government won't be able to pay all of its bills, causing at least a partial shutdown.
But there was no agreement in Congress late Monday, with just hours to go before hitting a shutdown deadline.
The Dow Jones industrial average fell 0.8 per cent to close at 15,129.67. The Standard & Poor's 500 fell 0.6 per cent to 1,681.55. The Nasdaq composite fell nearly 0.3 per cent, to 3,771.48.
Benchmark oil for November delivery was down 36 cents to $101.97 per barrel in electronic trading on the New York Mercantile Exchange. The contract grade fell 54 cents to close at $102.33 a barrel on the Nymex on Monday.
In currencies, the euro rose to $1.3528 from $1.3522 late Monday. The dollar rose to 98.49 yen from 98.28 yen.
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