Markets in China are closed for a weeklong holiday. Markets in South Korea also were closed.
Oil prices gained and US futures were higher as the threat of a US federal government shutdown receded after Congress approved a temporary funding bill late Saturday to keep federal agencies open until November 17.
Japan's Nikkei 225 index advanced after a central bank survey showed business confidence on the rise.
The Bank of Japan's "tankan" quarterly survey measured business sentiment among major manufacturers at plus 9, up from plus 5 in June.
Sentiment among major non-manufacturers rose four points to plus 27, in the sixth consecutive quarter of improvement and the most positive result in about three decades.
In Tokyo, the Nikkei 225 index was up 0.7 per cent at 32,098.40. Australia's S and P/ASX 200 lost 0.2per cent to 7,037.90. Taiwan's Taiex gained 1.2 per cent, while the SET in Bangkok edged 0.1 per cent lower.
On Friday, Wall Street closed out its worst month of the year with more losses. The S and P 500 slipped 0.3 per cent to 4,288.05 and the Dow fell 0.5 per cent to 33,507.50. The Nasdaq composite edged 0.1per cent higher, to 13,219.32.
After easing earlier in the day on encouraging signals about inflation, Treasury yields got back to rising as the day progressed.
The yield on the 10-year Treasury yield returned to 4.58 per cent, where it was late Thursday, after dipping to 4.52 per cent.
It's again near its highest level since 2007.
Treasurys are seen as some of the safest investments possible, and when they pay higher yields, investors are less likely to pay high prices for stocks and other riskier investments.
That's a big reason why the S and P 500 dropped 4.9 per cent in September to drag what had been a big gain for the year down to 11.7 per cent
Treasury yields have been climbing sharply as Wall Street accepts a new normal where the Federal Reserve is likely to keep interest rates high for longer.
The Fed is trying to push still-high inflation down to its target, and its main tool of high interest rates does that by trying to slow the economy and hurting prices for investments.
The Fed's main interest rate is at its highest level since 2001, and the central bank indicated last week it may cut interest rates next year by less than it earlier expected.
Friday's economic data showed that not only was inflation a touch cooler than expected in August, so was growth in spending by US consumers.
That can be a positive for inflation but it may also dent what's been a big driver keeping the US economy out of a recession.
The resumption of US student-loan repayments also may funnel more dollars away from the spending by consumers that has helped to keep the economy afloat.
Oil prices have jumped to their highest level in more than a year, which is pressuring the economy by raising fuel costs for everyone.
Early Monday, a barrel of US crude was up 31 cents to USD 91.10 per barrel in electronic trading on the New York Mercantile Exchange. It sank 92 cents Friday to settle at USD90.79, but it's still up sharply from USD 70 in June.
Brent crude, the international standard, rose 27 cents to USD 92.47 per barrel.
The latest monthly update on the US jobs market is due this week, with a couple of important reports on inflation coming the following week.
Postponements of such reports could complicate things for the Fed, which has insisted it will make upcoming decisions on interest rates based on what incoming data say about the economy. The Fed's next meeting on rates ends on November 1.
In currency trading Monday, the dollar rose to 149.79 Japanese yen from 149.38 yen. The euro slipped to USD 1.0572 from USD 1.0589. (AP) FZH
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