Oil prices gained to stay above $87 per barrel amid optimism American leaders can reach a budget deal and avoid automatic tax and spending cuts that might dampen growth.
Tokyo's Nikkei 225 added 1 percent to 9,928.07, adding to the previous session's 0.9 percent gain. China's benchmark Shanghai Composite Index added 0.1 percent to 2,160.74 and Hong Kong's Hang Seng gained 0.2 percent to 22,555.2.
Sentiment in China was supported by signs the world's second-largest economy is emerging from its deepest slump since the 2008 global crisis. Optimism was boosted by last weekend's pledge by new Communist Party leaders to support a recovery with more spending and easy credit if needed. They also promised reforms aimed at expanding private business.
"The economic recovery is gaining further traction, particularly supported by improvement in domestic demand conditions," said JP Morgan economists Haibin Zhu and Grace Ng in a report.
In Japan, markets gained following the weekend election victory of the Liberal Democratic Party, whose leader, Shinzo Abe, in line to become prime minister, wants to shore up growth with higher public works spending. That was despite concern about the consequences of adding to Japan's towering public debts and doubts about the effectiveness of looser policy.
The LDP's campaign platform rejecting "rational measures that might restore fiscal balance" suggests a new government "will lead the nation into an economic and-or financial `event' that will scar its prosperity for a long time to come," said Carl Weinberg of High-Frequency Economics in a report.
Elsewhere in Asia, Seoul gained 0.2 percent to 1,986.28. Singapore was up 0.4 percent at 3,170.94 and Australia's S&P/ASX 200 added 0.7 percent to 4,606.5. Taiwan's Taiex was little changed at 7,627.41.
Investors were watching negotiations in Washington over the U.S. budget and the impending "fiscal cliff" of automatic tax increases and spending cuts at the start of next year.
"U.S. markets managed to gain ground as some investors remained optimistic about the fiscal cliff negotiations" despite reports a settlement might be delayed until January, said Australia's IG Markets.
On Wall Street, the Dow Jones industrial average closed up 0.7 percent at 13,223.70. The broader S&P 500 index rose 1 percent to 1,427.22.
In Europe, Britain's FTSE 100 index closed down 0.2 percent at 5,912.15 while Germany's DAX edged 0.1 percent higher to 7,604.94. The CAC-40 in France slipped 0.1 percent to 3,638.10.
In currencies, the dollar was flat at 83.89 yen while the euro rose to $1.3174.
Benchmark crude for January delivery was up 33 cents to $87.53 a barrel in electronic trading on the New York Mercantile Exchange. The contract added 47 cents on Monday to settle at $87.20.