Record closes on Wall Street and upbeat economic data that lifted US Treasury yields and the dollar, even as weaker oil prices took their toll on energy stocks, also help lift Asian shares on Tuesday.
Futures suggested an firm start to the European trading day, with the Eurostoxx 50 STXEc1 up 0.3 percent and FTSE futures FFIc1 up 0.1 percent.
MSCI’s broadest index of Asia-Pacific shares outside Japan MIAPJ0000PUS was 0.4 percent higher in afternoon trade, clawing back losses from earlier in the Asian day.
Japan's Nikkei stock index ended up 1.1 percent as a tailwind from a weaker yen helped power it to its highest levels since August 2015. Markets in China and South Korea were closed for holidays.
Hong Kong's Hang Seng index rose 1.9 percent as trading resumed following a public holiday on Monday, led by mainland banks and insurers after China's central bank cut reserve ratios over the weekend to encourage lending.
Australian shares slipped 0.5 percent, pressured by financial and energy shares. The energy index .AXEJ, which has moved largely in tandem with the main index in recent sessions, skidded 1 percent in line with weaker crude prices.
As widely expected, the Reserve Bank of Australia kept interest rates on hold at a record low of 1.5 percent. The RBA said a stronger local currency would slow the economy and restrain price pressures.
The dollar index, which tracks the greenback against a basket of six major rivals, added 0.3 percent to 93.839 .DXY, after nudging up to its highest levels since August 17.
The euro eased 0.2 percent to 1.1709 US dollar, facing pressure from Spain's biggest constitutional crisis in decades, after Sunday's violence-marred independence referendum in Catalonia opened the door for its wealthiest region to move for secession as early as this week.
Proposed US tax code changes as well as the possibility that US President Donald Trump will appoint a more hawkish Fed Chair also gave the dollar a lift.
Crude oil futures extended losses after tumbling on Monday, as a rise in US drilling and higher OPEC output put the brakes on their recent rally and rekindled concerns about oversupply.
“The fourth quarter is not too kind to the price of oil, as we switch from summer demand to expectations of winter demand,” said Jonathan Barratt, chief investment officer at Ayers Alliance in Sydney.
On Wall Street on Monday, US stocks started the fourth quarter on a strong note, with all three major indexes closing at record highs after data underscored strength in the economy. The Institute for Supply Management index rose to 60.8 in September, from 58.8 in August, exceeding expectations for a reading of 58.
US construction spending also rebounded in August after two straight months of declines, boosted by increases in both private and public outlays.