Uncertainty about the outcome and worries that the winner might not be known for days has led to warnings that investors could be in for a period of volatility.
Eyes will also be on the Federal Reserve's policy decision on Thursday, with expectations for another cut, while the post-meeting statement from bank boss Jerome Powell will be pored over for an idea about its plans for 2025.
A win for Republican Donald Trump is expected to boost the dollar, restoke inflation and send Treasury yields higher owing to his pledges to slash taxes and impose tariffs on imports.
But analysts see less upheaval from a win by Democratic Vice President Kamala Harris.
"Some view a second Trump term as a potential ticket to higher deficits and a dash of inflation, courtesy of his tax-and-tariff playbook," said Stephen Innes at STI Asset Management.
"A Trump victory with a Republican Congress would likely mean a green light for these pro-growth, deficit-stirring policies.
"With Harris and a divided Congress, radical Democratic policies would face a wall, keeping fiscal volatility in check compared to Trump's economic flamethrower."
He added that a Trump win and Republican sweep of both houses of Congress could cause headaches for Powell as he continues his battle to bring inflation to heel.
National Australia Bank's head of market economics, Tapas Strickland, said that after Thursday's decision: "Harder discussions come in December and beyond, especially on the pace of potential cuts, where rates are likely to go, and any policy impacts by the next president and Congress."
Wall Street's three main indexes ended in the red, and Asian traders battled to build on their broadly positive Monday performance, with markets swinging in and out of positive territory.
Hong Kong and Shanghai rose as traders await the end of a 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.
Tokyo rallied more than one percent as investors returned from an extended weekend, while Wellington, Taipei, Jakarta and Manila also advanced. Sydney, Singapore and Seoul edged down.
Oil prices inched down after surging almost three percent Monday after top producers agreed to extend output cuts through to the end of December and on worries about the Middle East crisis.
- Key figures around 0230 GMT -
Tokyo - Nikkei 225: UP 1.1 percent at 38,474.66 (break)
Hong Kong - Hang Seng Index: UP 0.3 percent at 20,636.74
Shanghai - Composite: UP 0.4 percent at 3,322.02
Euro/dollar: DOWN at $1.0875 from $1.0878 on Monday
Pound/dollar: UP at $1.2957 from $1.2954
Dollar/yen: UP at 152.33 yen from 152.17 yen
Euro/pound: UP at 83.96 from 83.94 pence
West Texas Intermediate: DOWN 0.1 percent at $71.42 per barrel
Brent North Sea Crude: DOWN 0.1 percent at $75.02 per barrel
New York - Dow: DOWN 0.6 percent at 41,794.60 (close)
London - FTSE 100: UP 0.1 percent at 8,184.24 (close)
dan/cwl
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