Traders work on the floor of the New York Stock Exchange (NYSE) in New York City. AFP
Wall Street's main indexes, which had fallen the previous day, rebounded after voting began in the world's biggest economy.
In Europe, London dipped 0.1 percent as investors await an interest-rate decision by the Bank of England on Thursday while Paris and Frankfurt ended the day with modest gains.
Equities in Shanghai and Hong Kong won strong support from hopes over China's economy.
The dollar weakened against the euro, the British pound and the yen.
Kathleen Brooks, research director at XTB, said markets have priced in a victory by Donald Trump and thus a win by Kamala Harris would be a surprise that causes short-term volatility.
"A win for Harris could lead to a short term sell off in the dollar, gold and potentially in US stocks," she said in a note to clients,
"This could also boost global equities, as Harris is seen to be less tempted to slap tariffs on imports. Chinese stocks could rally sharply, along with key European and UK firms."
A win for Republican Donald Trump is expected to restoke inflation and send Treasury yields higher owing to his pledges to slash taxes and impose tariffs on imports, which could push up the dollar.
Analysts see less upheaval from a win by Democratic Vice President Kamala Harris.
"A pro-tariff Trump presidency could see the dollar strengthen amid concerns higher inflation will prompt the Fed to keep interest rates higher," predicted Matt Britzman, senior equity analyst at Hargreaves Lansdown.
"There is likely to be a period of volatility particularly if the result is contested, but investors should keep their eyes on long-term horizons as historically financial markets have risen over the course of both Democratic and Republican presidencies," he added.
Fawad Razaqzada, analyst at City Index and Forex.com, said that "traders are not committing to any particular direction across financial markets, and you can't really blame them."
Given that the race appears to be a toss-up "this makes it extremely difficult to make a strong case for the direction of the dollar or stocks this week," he added.
Investors are also awaiting another US Federal Reserve rate cut on Thursday as inflation cools.
Asia up
Hong Kong and Shanghai each closed up by more than two percent Tuesday after data showed China's services sector expanded last month at its fastest pace since July.
The news came as traders await the end of a Chinese government meeting this week to hammer out an economic stimulus.
Officials are expected to give the go-ahead to about $140 billion in extra budget spending, mostly for indebted local governments, and a similar one-off payment for banks.
Chinese Premier Li Qiang, meanwhile, said he was "fully confident" that China's economy would hit its growth targets this year and indicated that there was room to do more.
Oil prices rose, but less sharply, having surged almost three percent Monday on worries about the Middle East crisis and as top producers agreed to extend output cuts through to the end of December.
On the corporate front, Boeing shares fell slightly even though striking workers approved a contract proposal late Monday, ending more than seven weeks of stoppages that underscored discontent in the workforce of the beleaguered US aviation giant.
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