Oil and copper also firmed on the prospect of progress in the U.S. budget talks, but expectations of more monetary easing in Japan kept the yen soft.
President Barack Obama is seeking higher tax revenues which include increased rates on the wealthy while he is willing to cut some spending by changing the way cost of living adjustments are made to Social Security retirement benefits and other programs.
Obama's offer shows his willingness to give way on an item that some of his supporters had sought to protect, and may help advance negotiations with top Republican John Boehner to avert the fiscal cliff before the end-year deadline.
MSCI's broadest index of Asia-Pacific shares outside Japan <.miapj0000pus> was up 0.2 percent, following a rise in global shares on Monday. The index snapped an eight-day winning streak on Monday as investors took profits from last week's rally.
Fears over the U.S. fiscal crisis have dragged on many markets, but regional equities took direction from local factors.
Australian shares <.axjo> led Asia's outperformers with a 0.7 percent gain, lifted by a rise in iron ore prices <.io62-cni> to a five-month high.
"Iron ore is a very key commodity in the Chinese industrial machine, steel usage will bounce back and that is good news for our exporters," said Baillieu Holst director Richard Morrow.
Seoul shares <.ks11> rose marginally but underperformed others in Asia, as investors were reluctant to build positions ahead of South Korea's presidential vote on Wednesday.
In Japan, the Nikkei average <.n225> surged 1.1 percent to an 8-1/2-month high and edged closer to the key 10,000-mark, with sentiment bolstered by a landslide election win for the conservative Liberal Democratic Party on Sunday. <.t>
LDP leader Shinzo Abe, who is due to be confirmed as Japan's next premier on December 26, is calling for far more aggressive monetary stimulus and huge public works spending to rescue Japan out of decades-long deflation, pledges which are seen pressuring the yen and supporting Japanese stocks by improving earnings for Japanese exporters.
"The Nikkei is up today primarily due to the rise in U.S. stocks overnight, but the 'Abe-effect' is surprisingly longer-lasting as investors seem to be postponing the timing of unwinding their positions until they see the details and specifics in policies," said Ayako Sera, market economist at Sumitomo Mitsui Trust Bank.
YEN REMAINs PRESSURED
The dollar inched up 0.1 percent to 83.95 yen, off a 20-month high of 84.48 yen hit on Monday but well above its late New York levels on Friday.
Abe applied fresh pressure on the Bank of Japan on Monday, saying that the election result reflected strong public support for his views, which he hoped the BOJ would take into account at its two-day policy meeting starting on Wednesday.
"The dollar has more upside against the yen ahead of the BOJ's meeting, with expectations for some additional easing steps being strengthened after Abe's comments yesterday," said Yuji Saito, director of foreign exchange at Credit Agricole in Tokyo.
"The corrective fall in the dollar/yen after the election was small and it's crawling up because the yen weakening trend is still intact. But after the BOJ meeting, there will likely be pre-holiday profit-taking, pushing the dollar/yen down by 1 to 2 yen," he said, adding that the dollar could temporarily touch 85 yen before profit-taking sets in by the end of the year.
The benchmark 10-year Japanese government bond yield hit a one-month high of 0.750 percent on concerns that big-scale fiscal stimulus could seriously increase the country's debt burden.
U.S. Treasury yields also inched up in Asia, with the 10-year yields briefly reaching 1.796 percent, its highest level since October 26, on hopes for a deal on the U.S. fiscal cliff.
London copper was up 0.2 percent to $8,078.50 a metric ton (1.1023 tons).
U.S. crude rose 0.4 percent to $87.57 a barrel and Brent added 0.5 percent to $108.18.
(Additional reporting by Victoria Thieberger in Melbourne; Editing by Eric Meijer)
