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MSCI's broadest index of Asia-Pacific shares outside Japan inched up 0.3%, with Australian shares rising 0.4% and South Korean shares opening 0.3% higher.
Japan's Nikkei stock average opened down 0.2%, with Japanese markets resuming trading after a holiday on Monday.
The formation of a government in Italy ended a two-month political vacuum in the euro zone's third-largest economy, bringing Italy's five- and 10-year borrowing costs down to their lowest level since October 2010 at a bond sale and boosting European shares on Monday.
New Prime Minister Enrico Letta promised to push for a change to Europe's focus on austerity and pursue growth.
The euro held steady around $1.3095.
In the US, the Standard & Poor's 500 Index closed at a record high on Monday, as investors saw that a recent batch of mixed data and soft inflation offered little reason for the US Federal Reserve to change its very accommodative stance at its two-day meeting ending on Wednesday.
The European Central Bank, on the other hand, is expected to cut the euro zone's main interest rate by 25 basis points at its meeting on Thursday, given a deteriorating European economy.
Barclays Capital said in a research note that expectations of low policy rates will continue, while expectations of ongoing central bank support and soft inflation have driven US and European equities higher.
"Given the underlying inflation trends, we believe attention should shift to the potential for further accommodation, which may involve increasing the monthly pace of purchases, holding securities for longer, or modifying the forward guidance," Barclays Capital said.
Barclays said it expected the Fed to keep its current policy stance while the ECB was likely to lower interest rates.
Expectations for aggressive deflationary policy in Japan has led to a sharp weakening of the yen over recent months. While industrial output grew more slowly than expected at 0.2% in March from the prior month, manufacturers expected output to pick up to 0.8% in April.
A gauge of Japanese manufacturing activity expanded in April at the fastest pace in just over a year, signalling that stabilising overseas demand and a weaker yen are helping the economy.
The dollar was up 0.2% at 97.93 yen. While the dollar has retreated from a four-year high of 99.95 yen reached earlier this month, it has mostly stayed above 97 yen since the Bank of Japan introduced its unprecedented plan in early April to double the monetary base in two years to achieve 2% in that time.
US consumer spending rose unexpectedly in March, temporarily boosted by demand for energy due to colder weather, but an index of consumer price inflation fell for the first time since November, underscoring the economy's weakness.
Data on US housing market continued to improve, with a private-sector report on Monday showing signed contracts to buy previously owned homes rose 1.5% last month to the highest level since April 2010.
US crude was down 0.2% at 94.35 a barrel early in Asia on Tuesday.
