 "Asian shares post gains, China worries linger")
The dollar stepped back from three-year high against a basket of currencies as its strong rally sparked by strong US employment data last Friday ran into profit taking, though analysts think its uptrend is intact.
Japan's Nikkei share average rose 1.2% in early trade, edging close to the six-week high hit on Monday, while South Korea's Kospi index rose 0.6%.
"The market remains sensitive to Chinese shares. The Nikkei's performance will depend on how the Shanghai market moves," said Yoshiyuki Kondo, an analyst at Daiwa Securities.
Asian shares have been hit by a double whammy of worries over slowdown in China and tighter US monetary policy.
China shares had their worst day in two weeks on Monday, after China's leadership laid out plans to ensure banks would support an economic rebalancing to efficient high-end manufacturing from industrial overcapacity and extravagant investment funded by cheap debt.
"It is emerging market shares, rather than US shares, that have taken the brunt of a likely reduction in the Fed's asset purchase. If US bond yields are higher, investors do not need to go to emerging market for yields," said Ayako Sera, senior market economist at Sumitomo Mitsui Trust Bank.
"We are going to see a tug of war between strong US shares and softer emerging economy shares. The ultimate question is whether tighter US policy will damage emerging economies to the extent that it will hurt global growth," she added.
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An immediate focus for Asian traders is China's consumer and producer prices data for June is due at 0130 GMT.
Wall Street shares extended their bull run on Monday, with Standard & Poor's 500 Index gaining 0.53% to 1,640.46, supported by the brightening economic outlook after a solid payroll report on Friday.
After the market's close, Dow component Alcoa Inc , the largest US aluminium producer, reported a larger-than-expected quarterly profit, excluding one-time items such as restructuring costs and legal expenses, kicking off the earning season.
Its stock slipped 0.1% after hours, after having risen 1.4% in the regular session.
The dollar index, which measures the value of the greenback versus a basket of six major currencies, stood at 84.294, off Monday's high of 84.588, its strongest since July 2010.
"On the whole, the dollar is likely to gain further and US yields are likely to rise given the Fed's policy outlook," said Sumitomo Mitsui Trust's Sera.
Expectations the US economy is outperforming the rest of the world and that the Fed will reduce its bond-buying have sparked a nearly 5% rally in the dollar since mid-June, prompting some traders to say the move had been too fast.
US Treasuries prices likewise climbed on buying by bargain-minded investors, helping to bring benchmark yields down from near two-year highs.
The yield of 10-year notes stood at 2.647%, off Monday's high of 2.755%.