Shares have rallied this week as traders piled bets on Joe Biden winning the White House, with opinion polls showing him with a big national lead though with slim advantages in battleground states.
Speculation is that counting in Pennsylvania -- which could be the decider -- might not be called until possibly Friday.
Still, in a brief speech, Biden expressed confidence he will win but warned the result could take time, with Trump immediately hitting back accusing the challenger of trying to steal the election.
While Tuesday was formally Election Day, in reality, Americans have been voting for weeks. The Covid-19 pandemic caused a huge expansion in mail-in and early voting, and nearly 100 million people had already cast their ballots, though many of those will not be counted until polls close.
"Markets have taken a step back from the Democratic sweep scenario -- though are not yet giving up on it," said Axi strategist Stephen Innes.
"Biden is still favoured to win the presidency, but we now could be heading towards a delayed confirmation of the winner of the election, which is probably the worst-case scenario for risk."
- Alibaba shares sink -
Tokyo led gains, jumping 1.7 percent, Sydney piled on 0.9 percent while Shanghai, Seoul, Mumbai, Wellington, Bangkok and Jakarta were also up. Taipei gained one percent and Manila rallied two percent.
However, Hong Kong was flat and Sydney fell.
"The extent that investors were hoping either for quick clarity or massive fiscal stimulus, those hopes are being pared back," said Max Gokhman at Pacific Life Fund Advisors.
And Erika Karp, founder and CEO of Cornerstone Capital Group, warned that "the closer the race is, the bigger the risk is".
She added: "A close outcome is a risk to the market. The longer it drags out, the bigger the risks."
Still, while a failure for Biden and the Democrats would jolt markets, the general consensus is that whoever wins will still push through a major stimulus package for the struggling US economy as it battles the virus.
In Hong Kong, tech titan Alibaba sank more than seven percent after China's shock, last-minute decision to suspend the world-record $34 billion IPO of its fintech arm Ant Group less than 48 hours before it was due to debut.
Shanghai's stock exchange announced the suspension late Tuesday, a day after founder Jack Ma was summoned by regulators amid growing official pushback against the company.
The Shanghai exchange cited "major issues such as changes in the fintech supervisory environment" that it said raised concerns over whether Ant Group could now meet listing requirements.
- Key figures around 0610 GMT -
Tokyo - Nikkei 225: UP 1.7 percent at 23,695.23 (close)
Hong Kong - Hang Seng: FLAT at 24,933.78
Shanghai - Composite: UP 0.1 percent at 3,275.11
Euro/dollar: DOWN at $1.1659 from $1.1711 at 2115 GMT
Dollar/yen: UP at 104.88 yen from 104.52 yen
Pound/dollar: DOWN at $1.2989 from $1.3035
Euro/pound: DOWN at 89.75 pence from 89.82 pence
West Texas Intermediate: UP 2.4 percent at $38.56 per barrel
Brent North Sea crude: UP 2.3 percent at $40.62 per barrel
New York - Dow: UP 2.1 percent at 27,480.03 (close)
London - FTSE 100: UP 2.3 percent at 5,786.77 (close)