The MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.3%.
Australian shares rallied 0.8% to a fresh 21-month high led by shares in the financials sectors as the US S&P 500 index closed above 1,500 for the first time since 2007. Australian markets were closed on Monday for a holiday.
South Korean shares opened up 0.3% after touching an 8-week low the day before.
The benchmark Standard & Poor's 500 Index eased slightly on Monday after an eight-day winning run but held above 1,500, after closing above it on Friday for the first time in more than five years.
Risk appetite has been improving overall with US earnings generally solid. A rise in a gauge of planned US business spending in December added to a recent run of positive global economic data, and signs of easing financial stress in the euro zone. Euro zone blue chips touched fresh 18-month peaks on Monday.
More solid US growth indicators would, however, fuel speculation the Fed may mull pulling back on aggressive easing stimulus. The Fed ends a two-day policy meeting on Wednesday. The first estimate of US fourth-quarter gross domestic product will be released on Wednesday, followed by non-farm payrolls on Friday.
"Ahead of key events, markets are likely to stay in ranges. But with yields on US Treasury and German government bonds inching higher, one might say investors may be shifting funds to riskier assets from safe-havens," said Yuji Saito, director of foreign exchange at Credit Agricole in Tokyo.
"That's part of the reason why the euro has stayed firm," he said. Saito said while a rise in US yields underpins the dollar against the yen, they were likely to be capped with end-month selling from exporters and options lined up between 90.50 and 91.50 yen.
The benchmark US 10-year note briefly pierced 2% on Monday for the first time since last April.
Japan's Nikkei stock average opened down 0.7% after striking a fresh 32-month high above 11,000 on Monday.
The dollar fell 0.3% to 90.53 yen after touching 91.32 on Monday, its highest level since June 2010, while the euro also eased 0.3% to 121.75 yen from Monday's high of 122.91, its highest point since April.
