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The MSCI's broadest index of Asia-Pacific shares outside Japan was down 0.2%, with Australian shares falling 0.4% on lower metal prices.
South Korean shares opened up 0.1% after financial markets were closed on Friday for a holiday.
Japan's Nikkei stock average opened 0.8% higher as a wealer yen helped buoy sentiment.
"The KOSPI is seen continuing gains from last week as additional talks are expected concerning the US 'sequestration', while the yen's previous rapid weakness is seen getting milder," said Han Chi-hwan, an analyst at KDB Daewoo Securities, of Seoul shares.
South Korea's manufacturing activity expanded in February at the strongest rate in nine months as new export orders rose by the sharpest pace since the second half of 2011, a private survey showed on Monday.
A private gauge of Australian inflation showed price pressures moderated in February, helped by falls in travel and clothing costs, indicating there was still scope for cuts in interest rates if needed to support the economy.
The dollar eased, but was still near Friday's six-month high against a basket of currencies.
Despite the wide-ranging US spending cuts that automatically kicked in on Friday, the US currency was bolstered by surprisingly strong manufacturing and consumer sentiment which lifted US equities higher in contrast to a weak close for other global equities and the euro on Friday.
Evidence of Europe's problems, with Spain also at risk of needing a state bailout, came on Friday as data showed that Germany and Ireland were the only two euro zone members with factory output growth last month. Joblessness in the euro zone rose to an all-time high.
The euro steadied around $1.3020, after slipping to a low of $1.2966 on Friday, its lowest in nearly 3 months.
Over the weekend, China said growth in the country's increasingly important services sector expanded at its slowest pace in five months in February, reinforcing the view that the recovery in the world's second-largest economy remains modest.
The data followed Friday's figures showing China's factory growth cooled to multi-month lows in February. But economists said the sluggish data did not point to a risk of Beijing sliding back into recession.
"The February PMI in China suggests growth stabilization and is consistent with reduced concerns about a hard landing," Barclays Capital said in a note. It added that the sequestration cuts will remain a major theme for the market in the coming weeks.
Just hours after across-the-board spending cuts officially took effect, President Barack Obama pressed Congress on Saturday to work with him on a compromise to halt a fiscal crisis that threatens both the economy and his broader domestic policy agenda.
Concerns about the negative economic impact from the US spending cuts pushed oil prices lower on Friday.
US crude was down 0.1% early on Monday to $90.56 a barrel.
A stronger dollar hurt gold, leading bullion down on Friday for its third straight weekly decline. Spot gold was up 0.3% to $1,579.91 an ounce early on Monday.
