Onshore China shares ended marginally higher to post a third-straight gain, with the financial sector strong as retail investors chased large cap counters on hopes that the current rally runs through into the new year.
In the mainland, the CSI300 of the top Shanghai and Shenzhen listings closed up 0.1 percent, while the Shanghai Composite Index also edged up 0.1 percent to to 2,162.4. Both indexes are at their highest since August.
Hong Kong shares slipped for a second straight day, pulled lower by a 3.3 percent loss for AIA Group after American International Group sold its remaining stake in the Asian insurance giant.
The Hang Seng Index closed down 0.1 percent at 22,494.7. The China Enterprises Index of the top Chinese listings in Hong Kong edged up 0.1 percent.
AIA Group slid to HK$30.60 at the resumption of trade after American International Group sold its remaining stake in AIA for $6.45 billion. The deal was priced near its top end at HK$30.30 per share after it had been marketed at HK$29.65-HK$30.65 apiece.
Chinese property plays were hit by data that showed home prices in China's 70 major cities rose in November for the fourth month in the last five. The continuing strength of home prices makes it unlikely that Beijing will relax property market curbs any time soon. China Overseas Land shed 1.9 percent.
Seoul shares climbed on Tuesday, lifted by hopes for a U.S. deal on its budget stalemate, and as investors awaited the results of South Korea's presidential vote on Wednesday.
The Korea Composite Stock Price Index (KOSPI) rebounded 0.5 percent at 1,993 points.
Analysts said the election result is unlikely to have a major impact on Korean stock markets, which are often affected more by external factors such as the global economy than domestic ones.
Shares in Korean Air Lines were up 2.3 percent after the flag carrier abandoned its bid for an estimated $1.1 billion stake in Korea Aerospace Industries (KAI). Shares in KAI , the country's sole aircraft maker, fell 3.2 percent on the news.
LG Household & Healthcare gained 2.9 percent after acquiring a Japanese firm to expand in the world's second largest beauty market.
Panel-maker LG Display rose 2.4 percent following two days of sharp losses.
Korean markets will be closed on Wednesday for the presidential elections.
Australian shares came off session highs to close up 0.5 percent on Tuesday to a 17-month high, boosted by hopes for further rate cuts and optimism about U.S. budget talks.
The benchmark S&P/ASX 200 jumped 21.8 points to 4,595.2.
Mining stocks led the index higher with Rio Tinto up 1.8 percent, Atlas Iron up by 5.2 percent and Northern Iron increasing 9.5 percent. Uranium miners extended gains after the pro-nuclear power Liberal Democratic Party won Japan's election. Paladin Energy jumped 6.7 percent.
Shares of mining exploration firm Cape Lambert Resources surged10.4 percent after announcing a buyback for up to 10% of shares early Monday morning.
Billabong shares remain on a trading halt pending the release of an announcement by the company. The Australian surf wear retailer requested the halt on Monday, ahead of a possible takeover bid for the company.
Australia's central bank said it decided to cut interest rates this month rather than wait because it saw further evidence that a peak in the mining investment boom was near, while the non-resource sector showed no signs of picking up.
New Zealand's benchmark NZX 50 index came off earlier session highs to end up 0.3 percent at 3,979.2 points.
New Zealand's government said it would maintain its tough spending controls in 20 years as it downgraded its economic growth outlook on Tuesday, pledging to return the strained budget to a small surplus by 2015.
In Southeast Asia, Singapore's Straits Times Index closed down 0.06 percent and Malaysia's KL Composite Index added 0.7 percent.
In India, the BSE Index was up by 0.6 percent whilst the 50-share NSE Index edged up 0.6 percent.