Asian equity markets were broadly higher on Tuesday, with stocks in Hong Kong and Japan leading gains to track overnight strength on Wall Street, thanks to upbeat U.S. data. The Hang Seng Index HSI, +1.63% opened the fourth quarter with a 1.6% gain, in part catching up to the region's gains on Monday, when the city's stock exchange was shut for a holiday. Markets in China and South Korea are closed for the entire week.

European stocks kicked off the week in an upbeat mood on Monday, getting a boost from a weaker euro that tumbled after violent clashes in Catalonia in Spain during the weekend's independence referendum.

U.S. stock benchmarks closed at all-time highs on Monday afternoon, as equities resumed a steady run-up that could set the tone for the final three months of 2017. Four main benchmarks set records: the S&P 500 index, the Dow, the Nasdaq and the small-cap Russell, shaking off a mass shooting in Las Vegas that President Donald Trump described as "an act of pure evil."